John:
Other than the "line of aim" observations that others are trying to point out, I think there's no difference in what happens to the cue ball related to stroke length, as long as other things remain constant.
What *does* affect the cue ball related to stroke, however, is the grip. Loose/wristy grip usually results in a lively cue ball. A tight/non-wristy grip has the opposite effect.
In fact, to really demonstrate the difference grip pressure makes, if you use a normal grip on a level cue when hitting an extreme draw shot, you get just that -- an extreme draw shot. Now, use a tight grip on that cue (and I mean a death grip), and hit the same shot, in exactly the same place on the cue ball, with the same power, using the same level cue. Really focus on keeping that cue level, don't allow the cue ball to deflect the tip, and follow through. Result -- most often, you'll "lift" the cue ball up off the table surface (without scooping!), and not get a draw shot at all.
That's the only thing related to the "stroke" that I can see has an effect on the cue ball -- the grip. Not the length of stroke or anything like that.
-Sean