Mary,
Even though Type III PFD's aren't required to roll you to a face-up position if you are unconscious, most of them will hold you there (face-up) if you are able to get to that position.
What I found (floating around in a pool in full gear), was that I had to
actively work to keep face up because of the flotation in the butt of my trap harness. That's a little scary.
This team is wearing rashies over their PFD's/harnesses: