It's not easy for people to escape a submerged vehicle in still body of water, especially if the vehicle flips. Add in a raging river tumbling everything around, pushing everywhere... Even if you were able to escape the vehicle I don't think your chances of making it to shore from the middle would be good.
I think once you are on the surface, your chances rapidly grow, even when its cold water with a lot of current. You still only have to manage to get 20-30m to the side out of the strongest current. The way to the surface in time to not suffocate might be the problem, especially out of a wildly tumbling car that smashes against rocks and stuff in the riverbed while being hurled on by a powerful current.