Back in the day when tribespeople had to hunt their totem animal, hunters usually had to undergo a cleancing ritual after that. Violation of some taboos could be dealt with in same way. Not unlike modern practices of repentance and penance. So it's a maybe. But that would requre him to at least survive the current predicament.
Judging by the pictures during the explanations, it looks like their bodies turn to ice when submerged in water. Puts the "would you jump in after me" before into a brand new context if that is the case.