Can it be much different than shooting at a moving object, unless you are actually actively running like hell? Imo, run or shoot, it's impossible to do both. Most people can't even walk and text at the same time. I have seen people trip on smooth floors as the sip their coffee. Once, I saw a woman approach a door that was too clean. The door was open. She wasn't paying attention.
She missed the entrance, slammed into the door itself and hit the ground.. oh, she realized that she hit the door. Obviously shaken, she pushed the door shut, believing that she was opening it. She slammed into the glass again, once again hitting the concrete.
A person may be able to learn how to shoot while moving, it will obviously have a positive impact on every aspect of life and concentration, but moving while shooting outside of a non emergency situation is futile and unwise. It just the same sort of dumb idea as trying to make sixty foot head shots during a stress fire situation on a target that won't be sitting still like a nice, cooperative piece of paper.