No, because it would make games less fun to become that realistic.
In Far Cry 3 you can dive head first, arms stretched out in front of you (fucking awesome), and in that case you shouldn't take damage. When bailing from a hang glider over water, falling hundreds of feet, ass first, arms flailing, you should take damage. Still not totally realistic, but it makes some amount of sense.
But yeah, depends on the game.