No they won't. Animations are already timer based (animation frames per second) so whether you're at 10fps or 100fps, at 10 animation frames per second, you still see ten animation frames go by in one second.
Also, in my opinion, you should really always use V-synced framerate and not make the assumption for any user that their PC isn't good enough. If you ever use any framerate other than V-sync rate, the display goes from gorgeously smooth to crappy and choppy. Keep your games looking nice