When mine get to laying heavy their oil glands go wacky. I'm well aware to keep a close eye, but a new duck owner might not realize it's even possible for a duck to drown!
Adult ducks can definitely drown..I've had a few instances where I've had to wrap ducks in a towel because they've appeared hypothermic and I've blown them dry with a blow dryer and held them until theit eyes appeared normal.
I've never had one on its back before..maybe she couldn't flip back...