Yes, it does affect a few things.
First, if you make a clearly goofy selection you'll get a Live Trigger Reward other than a potion. Why this is doesn't make any sense to me, but picking the right or logical answer won't net you anything. The rewards here are almost always cosmetic so you're not missing much of anything.
Second, some of the live triggers will result in a Paradox Ending. These are, simply put, bad endings to the game. When you come into a Paradox Ending there will be a short scene and you'll be dumped back to the Historia Crux.
The unique thing about FF 13-2 is that all of these choices can be replayed by closing and opening gates again. Everything in the zone gets reset other than key items and fragments. So if you're not satisfied with how your first choices turn out you can simply go through it again.