You don't say how big your cam is so no way to guess what it will take to move it. Servo City makes some large servo based cam mounts. There are large powerful servos available that could move most cams. That being said, have you done any simple testing to see if what you are trying to do is reasonable? The golf tourniments have the high end equipment to follow balls in flight and make it seem simple. One simple test would be to try to track the action only by using the cam video without any other visual references (cover your head with a towel so you can only see the video display). Some time back I made a joystick setup to control my servo based pan/tilt web cam. The cam moved quickly, but tracking anything moving fast just looking at the video from the cam is more difficult than it would seem.
You bring up some good points. I can say I do think its possible since I have had to run the camera myself a few times, and had to move it to follow the ball, while looking at a completely different screen (I also run the switcher, and stat program, and do color commentary). Its another reason I didn't want to use a joystick, since following the ball is as much feel as movement. I.e. When you hear the crack of the bat (which we can hear with our audio equipment) automatically start moving the camera in the expected direction. Using the camera zoomed out helps this, and usually we zoom in only once we got a clear indication where the ball will go.
You also make a great point about golf, but we have done golf, as well. Golf balls are allot harder to track with a camera. They are smaller, often further away, and worse of all once they get in the air, their is no frame of reference, no one to look to see where the ball is going. In baseball, or football if worse comes to worse you can always zoom out, and look at where everyone is looking and point the camera their
The camera itself doesn't weigh much, only about a 1.5 - 2 lbs.
Those mounts you mentioned from servo world, interest me greatly. In fact they look almost perfect, as long as the speed can keep up, again, were not talking about super speed here, and the further away things are the less speed the camera mount really needs. In fact the only time you really need allot of speed is when the ball is passing very close to the camera or crossing it view at 90 degrees.