Well, a lot of animation is art and can't really be separated from it. (Not quite 100% of it, there's some aspects that are more about code, but code alone won't get you there.)
I'd say that having a fun game and grabbing people's attention in the first place are two related but distinct things. You don't need the best art to be successful, strictly speaking. (Undertale and Baba Is You spring to mind. But don't copy their art styles either, obviously.) And the best art isn't necessarily the most complicated art--a simple style that takes shortcuts can work if it's distinctive and cohesive.
It's hard to give a straight answer on this. There isn't a firm "if you do better than this than you will definitely be successful and otherwise you will flop" bar. But I'd generally assume that being better at art helps, most of the time.