I think it depends on the state/country. In Greece, any sort of rebresther/scuba gear is strictly forbidden.Have a friend who works as a game warden, seeing how confusing the rules for hunting/fishing is but utilizing a rebreather he says is not illegal for fishing all they care about is size/quantity of catch compared to where your hunting at and time of year
Washington state doesn't care at all when spearfishing is in season.