There's only one way to find out. Turn the option on (which, confusingly, turns the animations off) and then see how it works for you.
I have animations disabled, and iOS seems smoother to me. At this point I wouldn't be able to measure battery life or real performance, because I've had them off for so long. But you know what? It doesn't even matter. I like them off. The animations get tiring to me after a while.
Give it a try.