What if Theon had sent a letter to Robb ?

[Terrorthatflapsinthenight9]

It's one of the changes in the show that I really appreciated, helped by Alfie Allen's amazing performance as Theon Greyjoy, one of the best in the show. In a scene of the second season just before the Ironborn invasion in the North Theon can be seen with a letter that he wrote to Robb, warning him about his father's plan to backstab him and invade the North, with a conflicted expression on his face before deciding to burn the letter and to go along with his biological family.

What do you think would have happened in the books if Theon had a similar moment, but with his love and care for Robb winning over his desire to earn the respect of his family and the Ironborn this time, and thus sent the letter to Robb ? 

What changes could there have been to the story of ACOK and after, with this letter being sent ? 

What could have happened to Theon afterwards ? How much would this have changed Robb, Bran, Catelyn and the rest of the Starks and northmen's story ? What for the Ironborn and rest of Westeros ?

[The Commentator]

Theon and Jon are the same sort of people. Their stories are the same, the intersection is Ramsay. Conflicted and emotionally confused men. 

[Arthur Peres]

Theon would have no way to send the letter, Balon blocked the ports and I doubt that he would trust Theon anywhere close to the ravens. So if Theon tried that he would be imprisoned by his father.

Without Theon taking Winterfell the IB invasion would fail for sure, Rodrik would deal with Ramsey then gather the army and push Asha back into the sea while Victarion is starved, poisoned and bleed by the Cragnoman, eventually Rodrik would also push them away.

Without Winterfell falling Bran and Rickon are not considered "dead", Catelyn does not free Jaime, Robb does not sleep with Jeyne, Roose will keep his options open.

Robb will still be in a losing position after Blackwater, he would still be fighting Lannisters, Tyrells, IB, Crowlands and the Stormlords, but he is not that weak, Red Wedding would probably not happen as Walder is not that pissed with him but would still try distant himself, if the purple Wedding still happen the odds of Robb improve by a lot or at the very least he can negotiate a peace with Tommen now that Joffrey is dead and his beef was with Joffrey.