He'll probably die. We'll just come right out and say that Theon is probably the last person we'd ever want defending us from a horde of icy undead monsters, especially if we can't walk. It's because of that, that we're especially nervous for Bran, who will be sequestered in the Godswood with Theon and the Ironborn to "protect" him during the battle. Oh, there's also the fact that the Night King wants to kill him above all others (casual), and he had a heart-to-heart with Tyrion telling him about his transformation into the Three-Eyed Raven, so the evidence is stacked high against Bran's chances of survival. We'll go out on a limb and say that while his body will likely perish, his mind and consciousness will continue on living in some other way, be it in a Weirwood tree or within animals nearby.