As you see, this question caused some confusion. Most people can't distinguish between acceleration and velocity.
Whether the stick is accelerating at the time of impact makes virtually no difference to what the cue ball will do on most shots. As mentioned above, if you want to play with minimum effort, the best time to hit the cue ball is when the stick is moving at top speed. That is exactly when the acceleration is zero by the definitions of acceleration and velocity.
Whether that's the best time to hit the ball when you take other factors into account is another matter. For certain special shots, something else is required. The best example I can think of is when the cue ball is 1/4 inch from the object ball and you have to shoot straight at it. This needs to be hit with a severely decelerating stroke, and there are several standard techniques to achieve this. Jump shots are another example where deceleration may help you to not double hit or trap the cue ball.
To get maximum power, it may be best to still be accelerating when you hit the ball, but this is only because if you hit the ball at peak speed your stroke might be too long for accuracy. This depends on the player's skill and technique. Watch videos of power nine ball breaks.
For standard shots, some players seem to use constant acceleration, some hit the ball at zero acceleration and others hit the ball somewhat before the peak velocity so there is still some acceleration. You can make hand-waving arguments to support each of these techniques. Unfortunately, no professional sports kinesiologist has looked into this, AFAIK.
There are several articles here:
http://www.sfbilliards.com/articles/BD_articles.html (look for "stroke") about various aspects of strokes including a list of types. Dr. Dave has some good discussions and measurements on his site as well.