All infantry types take damage on drop, even dedicated para units. Admittedly they tend to lose less guys and take less suppression, because of supposed better training.
Other infantry types tend to break necks all to often, but that is meant to compensate for the fact that the game allows vehicles to be dropped ready to go.
Also watch out on what ground they land: it is very hard to swim under a parachute or the land feet first with 80lb. pack in a rock garden. Oh, always better than head first!
