Even if Balon still invades the North, without Theon taking Winterfell, a lot of things change. The supposed deaths of Bran and Rickon are what lead to Robb seeking comfort from Jeyne, and Catelyn releasing Jaime in the hopes of getting her daughters back.
If Theon doesn't capture Winterfell, Robb still has the Freys and Karstarks (and presumably the Boltons) on his side, and Jaime as a hostage, which would really change the landscape of the war.
This is another misconception. Robb marrying Jeyne was stupid, yes, but it did not cause the Frey's betrayal. The Red Wedding, or something similar, would have happened regardless. And losing the Karstarks because of releasing Jaime didn't help at all, but it wasn't a determining factor either.
If he had kept his word and married a Frey, the only difference would be that the Red Wedding would have been his own wedding rather than Edmure's. While Robb going back on his word no doubt pissed off Walder, the reason he betrayed Robb is that Robb had already lost at that point and he wanted to be on the winning side. Robb was taking his army back north to fight the Ironmen. Nobody outright said it, but it was implied that he was giving up the Riverlands because he had no way of holding them. The Freys knew that with Robb's army gone, they would just be destroyed by the Lannisters unless they managed to convince Tywin they were on his side. And I don't doubt for a second that Tywin would have still given the go-ahead on the RW even if they still had Jaime.