One could hunt water-fowl with an AR, but I'd want a scope good enough to do head shots... and you can't shoot them sitting on the water anyway
One could hunt waterfowl, not water-fowl, with an AR, if one were okay with violating a Federal law.
The deal about head shots is ludicrous.
With a legal firearm, one often must shoot cripples on the water, especially in the wake of the stupid Federal law prohibiting lead shot for waterfowl.
Very few hunters would shoot a healthy bird on the water because it defeats the purpose of waterfowl hunting, but I've never heard of it being illegal.