Gerald Burrard conducted experiments in this back in the '20's/30's. They attached a steel pattern board to the side of a car, and had it drive past the shooter at various speeds. They could discern no difference in the shape of the pattern regardless of how fast the car was moving, or how hard the shooter was swinging the gun. The difference in the time of impact between the first pellet and the last pellet is minimal. If it weren't, the patterns would have a distinct oblong or oval shape, not round.
It strikes me that the gentleman was an already skilled shooter who'd naturally learned to compensate for the shot string from his own gun. I think the important thing is for the shooter to know that it's supposed to be there and I have a feeling that results will improve more quickly if the shooter does.