Yep.
Try 20 rounds at full rest, then run your ass off for 100 yards and try for the same group. Harder than you think. Add in return fire, and things get even more interesting, and difficult.
However, I would attempt to run to a position (hopefully cover), stop, then shoot. Shooting while running/walking is generally a waste of good ammo.
If I were in a gun fight that required me to run, the run would kill me well before the bullets.
