It wouldn't be handy but it'd be fucking cool. If you know the velocity and trajectory of the ball then on an unobstructed shot you could instantly display the updated position of the ball after it has been struck. The difficulty would be gauging things like back spin which aren't (I'm guessing) observable by the camera, but which have a drastic impact on where the balls end up.
Yes, predictions can greatly improve recognition performance. Not only can you focus the bulk of your computations on the expected region of interest, but you can also potentially reason about appearance (e.g., if you know the frame-rate/integration time of the camera and expected speed of the ball, you could get estimates about how much blur to expect). You could also better handle difficult cases, such as when balls strike each other (e.g., simple conservation of momentum estimates should greatly constraint possible hypotheses for ball positions).
