Probably. But, that being said, my geckos jump/fall from ridiculous heights and just sort of shake it off. If it hurts them, they're tough little buggers and they recover quickly.
mine have freaked out before and jumped from my hands randomly before. I'm 6 ft and they fell most of that distance and just shook it off. Leos are usually very careful about ledges and such and mine have proven that they are exceptional at getting down from high places with little or no help. For such small animals, they are rediculously strong and resiliant. One of my females managed to get out of her tank one day. I found her in my recliner, looking at me like "what....i was bored!". I freaked knowing she had to have fallen no less than 5 ft to get out of her tank.
Since the hammock is in the air, I don't think it matters which side to put it on. I usually have something like a lay box (which doubles as a humid hide) on the floor near the hammock so they can climb on top of the box and then into the hammock. If they fall, it's only a few inches to the box.