Okay, I had a waterbirth and it was wonderful for me, but I don't know if I'd do it again. My son got stuck as you describe after pushing for 2 1/2 hours. When he came out and up, he wouldn't cry and needed oxygen. Of course, his 2nd set of apgars were just fine and the mwives assured me there were/are no side effects.
So, no, they won't breath in water. But, in retrospect, it was pretty scary.
I guess I don't know if it would've been any different lying in a bed.
It's a tough call.
But...I would REALLY recommend using a tub that has a disposable liner. No question of left over bacteria, etc.