The main idea: Shadamy is as likely to happen as Sonamy.
Well, here is an article I wrote:

SonAmy?
Have Sonic Team given Amy absolutely no dignity? The girl runs after a boy and tolerates his indifference or annoyance towards her!! That’s preposterous.
In one magazine, it is revealed that Sonic does have feelings for Amy, but he's too shy to admit it. [link]
Though that magazine only states that the authors of that article went to Sonic Team. It's not official, not Sonic Team told us that.It could be thought of by some as quite "Odd" for Sonic because he is a generally out-there person saying with no problem what is on his mind.
But some could say that Amy brings out Sonic's "softer" side. It is also unknown when or why Sonic fell for Amy, or if he even truly has. Regardless, Amy will continue to chase Sonic for as long as she must.
But a girl can't date someone forever. Their relationship will have to come to some kind of an end.
Amy is literally the female version of Sonic in several ways. First, she is pink (which is the female counter for blue), she has a sidekick (Cream) and she is a hedgehog. She is also a polar opposite to him, at least where temperament is concerned, she is easily angered while Sonic is much more difficult to anger. Just like brother and sister.
Even if Sonic will ever condescend to her romantically (although I don’t really believe in that) I think, Amy would always be worried “Am I good enough for him? Won’t he run away?” and so on... I strongly dislike such Japanese attitude towards women.
From my point of view Sonic has nothing to give Amy. Yes, she tries to develop her skills for him to notice her. To catch him.
But she doesn't develop mentally, she doesn't grow up. Her personality through games went from good to worse. She's underrated.
And what does Sonic need her for? He has his freedom

And Shadow just deserves to be loved anyway. What is that an eternal life without love? A nightmare.

And behold, the most killing evidence against SonAmy ever!
Yuji Naka, the creator of Sonic the hedgehog himself said that Sonic will NEVER get married. Especially with Amy.
Here is the interview on Sega’s official site [link]
“Sega.com: We get a whole lot of letters on this one: Do you think Sonic and Amy Rose will ever get married?

Yuji Naka: There will be hardly be any chance, I bet. Amy will continue to pursue Sonic all the time, but Sonic will not ever get married. I think so, because I cannot picture the image of Sonic that he is married and has his children! Also, I feel it is a more Amy's style to always chase Sonic.”

Shadouge?
I know Shadow is sometimes paired up with Rouge. They have so much interaction in the games. But I believe that Rouge and Maria are not alike, or even similar.
Shadow and Rouge are more of companions, comrades. Yet Rouge becomes more selfless around Shadow... she likes Shadow, yes. But Shadow has never shown her much affection, has he? And Rouge has some story with Knukles (who is officially stated to be her crush), too. "
They're teammates in Sonic Adventure 2 and Sonic Heroes, and often work together. Rouge and Shadow are close friends, Shadow being one of the few people Rouge cares about other than herself (along with E-123 Omega and Knuckles the Echidna). But, it has also been announced by Sega that Rouge seems to have a crush on both Shadow and Knuckles.
In Sonic Battle, Rouge calls Shadow "not bad-looking" and "a prince," and also lets him stay with her when he is injured and lacks a place to stay. Moreover, in Sonic Adventure 2, Shadow saved her life when she was trapped in Security Hall. *What, basically, doesn't change much, he would have saved her anyway. That explosion was sudden. He acted instinctevely and as he said himself he was saving the chaos emerald*
And that famous quote Shadouge fans refer to all the time Eggman walks away and Rouge tells Shadow "Did you get that?".
Shadow replies: "Soon enough, Maria".
He wasn't talking to Rouge! He didn't mistake her for Maria! He was deep in thoughts, talking to himself. He just promissed his dead girl to find the chaos emerald asap and have his revenge on the people of the Earth for her. See it here - [link]
In Sonic X, when she first established the business transactions for helping Eggman and Shadow find the Chaos Emeralds, she seemed oddly interested in Shadow. However, she was interested in him mainly because of his close resemblance to Sonic and later finding out the he was the main part of her mission: to find out whether or not the claims of his being the "Ultimate Life Form" were true. From [link]
Shadow has a close relationship to Rouge the Bat, she is probably the closest friend he has had since the death of Maria. The two always look out for each other, as seen in Sonic Adventure 2, Sonic Heroes, Sonic Battle, Shadow the Hedgehog, Sonic 06, and other game titles. Near the end of the Dark Side story mode in Sonic Adventure 2, Shadow discovers Rouge is a spy for the GUN organization, however he still refuses to reveal this to Eggman, opting instead to allow the plan to go the way she chose to manipulate it. In Sonic 06, Rouge says that if the whole world were to turn against Shadow, Rouge would still fight by his side, and in Shadow the Hedgehog, after Shadow defeats Black Doom and destroys the Black Comet, Rouge wonders if Shadow is okay. From [link]
But does SHADOW care for her as she does for him? A big question. The only evidence is the song “This machine”, but remember, in Sonic Heroes, Shadow was thought to be an android.

“Sonic X”
...is not a cannon Sonic verse.
First of all I want to to tell you, why I think Sonic X is not a cannon. They use a Mary Sue character! Chris Thorndyke! Let me explain, they had a purpose to accommodate all of Sonic characters somewhere, that’s why Sonic just happens to land in the swimming pool of *attention* a lonely billionaire kid who wasn’t asleep at that time of the night, and who was brave enough to save an alien life form (Sonic is an alien in Sonic X) from his swimming pool. That doesn’t sound believable to me. And what happens next? Chrises’ grandfather just occurs to be a great scientist! And the money of Chrises’ parents are so easy of access that Tails even manages to build on them a flying robot- plane Tornado X. How’s that? And now back to Shadamy...
The creators of Sonic X series were well aware which pairing was more popular among fans! SonAmy of course, so they just replaced Amy in the Ark scene with that annoying Mary Sue – Chris!!! Have you spotted virtually any similarities between Chris and Maria? They are both humans and that’s all! Chris doing that wise talking and Shadow crying in front of HIM?! It just seems weird and OOC for both. With Amy in that scene, it was alright, because she always tried to help whenever possible, and unlike Chris had a story of her own life to tell Shadow.
They used cheap trickery!
If they didn’t – I think that would have meant no SonAmy.

Psycology of Shadow x Amy
Shadow has a tragic past. He is cold and lonely. No kind of entertainment or business won’t make him feel more needed, more useful. He suffered a great loss (or he thinks he did, that doesn’t really matter ). And the only thing that can make him want not to go after Maria, may be love. You can’t always live in the past, sometimes you just have to move on. And anyways he decided to leave his past behind in the end of "Shadow the hedgehog" game. So why not?
Amy is lonely too. Maybe it’s not noticeable at first sight. Yes, she has a lot of friends. She’s a social... hedgehog. Extravert. But there is a strong lust for love that lives in her. And Sonic has a little to offer her in this kind of interaction. He is too light-hearted and independent, too immature and maybe even not serious enough.
Amy is naïve, sometimes a bit cowardly, and that’s good. Shadow was designed to protect, so that’s good.
Amy can live selflessly. It’s even stupid of her – she forgets herself and does anything to become good enough for the person she loves, shares all the problems of her beloved... *I was talking about Sonic here* I think, she has what it takes to understand Shadow with time.

From the point of view of raw psychoanalysis – Shadow may like the girls who resemble Maria.
(Oedipus complex).

Now some lyrics
He’s an introvert, thing in himself. She’s an extravert, all what comes to her mind is on her tongue.
She’s a girl. He’s a man (male hedgehog)
She’s delicate, not experienced. He’s strong and not once beaten by life.
Opposites attract, not because there is a saying that states that, but because they can harmoniously supplement each other.

And the main reason – both characters have such a big reserve for self development.
Shadow never had a childhood and Amy never was loved. They have so much give each other, if only they will ever understand that.
Shadow is cold and self-restrained, Amy has to learn that. And Amy is nice and kind, she has a faith in the others, that’s what Shadow has to learn.

Official relationship and hints. *Shadamy*

“Amy Rose and Shadow have an oddly friendly-termed relationship. They seem to manage to be respectful to one another (though this could simply be because Amy is pleased by Shadow's efforts in helping save the world and the fact that Shadow is never rude to girls). In Sonic Adventure 2, they only interact twice, but each is rather significant. Amy first meets Shadow when she mistakes him for Sonic and hugs him from behind and Shadow just remains unfazed and calm. Amy demands his name when she realizes he is not Sonic, but he simply looks on quietly. It is a mystery if Shadow would've replied her if not for Eggman taking Amy into his own matters. Later in the game aboard the ARK, Amy meets Shadow again and this times does her part in helping by begging Shadow to save the world. At first, Shadow simply replies, strangely in a none-threatening and calm way, that it is pointless, but then Amy points out that despite people sometimes being selfish, they were still inwardly good and that saving them was right. Because of this, Shadow suddenly has a flashback of Maria begging Shadow to make people happy. When Shadow comes to his senses he goes off to fight the Biolizard telling Amy that he has to keep his promise to Maria and Her. Amy was also the only one to see Shadow's tear after he remembered that Maria wanted him to save the people that live on our earth(Sonic adventure 2), making her the only person to see him cry (with the exception of Chris Thorndyke). Amy and Maria have the same insight of things, thus this might be one reason why Shadow is 'nice' to her. Amy has also done nothing to earn Shadow's dislike or hate, which may be why he's respectful to her upon meeting.

Shadow shows a sense of manners to girls. He has never been foul to any femalecharacter except, perhaps, Marine the Raccoon. Shadow is also practically the only male character who did not consider Amy rather careless or a waste of time (like Silver did when he asked himself what on earth he was doing with her and Sonic, Knuckles and Tails who find Amy rather a distraction)”
From [link]

Amy has a small, yet firm bond with Shadow the Hedgehog. They first meet in Dark Story of Sonic Adventure 2 during the attack on Prison Island where Amy mistakes Shadow for Sonic and because of that hugs him. When she realizes her mistake a few seconds later she asks Shadow who he is, but Shadow doesn't answer, obviously because it was a retorical question. In Last story the two meet again at the ARK where Amy asks Shadow to help the others save the planet. At first he refuses, but Amy remains determined and in the end through her words manages to remind Shadow his promise to Maria. In Sonic Battle, it is further more shown that Amy is concerned about Shadow when she meets up with Rouge. When Rouge mentions that Shadow is staying at Club Rouge, Amy says, "Shadow? He's here too?" and then she asks Rouge to tell her what Shadow's conditions are for staying with her and gets upset when Rouge does not answer. Also in Shadow the Hedgehog after Shadow defeates Devil Doom, and Rouge askes if he's alright, Amy answers tone "I'm sure he's alright Rouge, after all he is Shadow".

Team Dark never fights Team Rose in Sonic Heroes.
From [link]

In “Shadow the hedgehog” game, you have the option of helping Amy Rose find Cream & Cheese(who were taken into a large castle by Eggman). Of course, Shadow gets the option of helping all the other characters in the Sonic series. Though this is the only time Shadow will get no benefit, and helps Amy only because he's concerned. You also get to fight an Eggman boss with Amy at your side.

It has been discovered that if you play as Dark until you get to Cryptic Castle[Amy's level], then remain hero for the rest of the game, the storyline is listed as "The Miracle of Love".

- At the end of the game, after Hyper Shadow defeats Black Doom, Rouge comments on how she hopes Shadow is alright. Amy, who has been staring up at Shadow with an amazed and dreamy expression, just smiles brightly, "I'm sure he's fine, Rouge. After all, he IS Shadow.". She was not concerned, because she KNEW he was okay, which is usually the sign of a very strong bond. This shows her faith and trust in the ebony hedgehog.

- It should also be noted that Amy[if the admin can remember correctly..] did not mention Sonic in the entire game, which is pretty surprising, considering her obsession for him.
From [link]

Conclusion
If Shadow will ever have a chance to get to know Amy better I think they have what it takes to be happy together. Even the love calculator agrees with me (here is a little research [link] )
Yet, he is immortal and it will cause much pain for him in the future, because Amy will die sooner or later, and he won't.

So viva Shadamy)

Comment, please! I want to know what you think about it.