That's not how flexible containers work. In the presence of increased pressure, the guts press against the diaphragm, which compresses the lungs.
I don't have to imagine what removing air from my lungs feels like: that is part of breathing! Anyway, this guy seems to do OK compressing his lungs even more:
If the increased pressure is high enough, your diaphragm and lungs are going to be in a world of hurt.
Physiological freaks aside, go too deep, and you're dead. Especially when you go from 1 bar to, say, 15 instantly, which is a situation that free divers do not expose themselves to.
You know that pain you get in your sinuses and ears and other air-pockets in your body when you swim to the bottom of the deep-end of the pool? That's from a pressure difference of like .3 bar. Now imagine something 10 times that.
