Actually, a study that some biomechanical researchers in Austria did at a Eurotour stop found that a large majority of shots were played with zero acceleration at impact -- the cue stick was coasting at the instant it hit the cue ball. That is the most efficient way to hit the ball, all else being equal.
However.... For the break shot the players mostly were still accelerating when the stick hit the ball. I don't think they concluded anything about the reason for this but I suspect that if max speed is your main goal, you want to keep accelerating for as long as possible.
Of course the cue stick must be accelerated at some point during the stroke or it won't be moving. Most shots require the stick to be moving.