Would your question be the same if you were running to make a groundstroke rather than a dropshot?
If you see that you may just barely have time to reach the ball- so, then do you wait until you get there to make preparation for a stroke? Well, to answer your questio- obviously not.
If at all possible, you want to be ready to do something with the ball once you get there. As you are moving, get your reacket out, back, up... wherever it needs to be, so you can volley, slice, drive, smash, topspin, lob, whatever... and then place the ball where it needs to go.