Yes, I've seen them. I've also seen major league batters spend 5 minutes in the box twitching and adjusting their sweatbands and helmet just so. Does that increase their batspeed?

If you still think swinging a heavy bat is the way to faster bat speed read this: Warming up with a weighted bat does not increase swing speed.

There's no question you can train on a fixed gear. You can also train equally well if not better on a regular bike. For example, if you want to do muscle tension intervals you want to find someplace where you can ride at 90-100% of FTP at 50-60RPM. You could do this on hills of a certain gradient with a fixed gear bike, but there are many more locations and conditions (i.e. headwind) that you can achieve this with a geared bike.