Probably not the camera you want for that. My daughter plays high school volleyball and I have tried in various gyms under all manner of light conditions and camera settings to get both action and stable shots with very mixed results, with most action shots being fails. That said, that type of photography is not this camera's forte and you really need a dslr with a good lens to do that job right.
No, the shutter speed is way too slow. I attempted to take photos at an adult birthday party and although most people were sitting down just talking to each other, I still had a bunch of blurred photos. Get a small Pansonic (fx 15 or 20) instead. Panasonics take fast pictures and are not that expensive!