The way I see it going down is Taim's faction in the BT will make a move against Rand as TG begins, so Logain runs off, slaughters most of them, drags the rest back to Rand and forces them to swear fealty. Would fit with Min's visions of glory for him. He'd be a huge hero because of it, not just to the Aes Sedai, but to everyone in general.