Yes, but chickens will enjoy a 4 or 6' high run a LOT more than a 2' high one. They like to stretch tall, flap, hop, even fly a little... indeed sometimes they feel they *need* to, to get away from each other.
As far as deciding on a design to build, it will be a great deal more pleasant and non-back-breaking for you to work in if you build the run 6' tall. You *can* bend over to catch birds, rake poo, etc in a 4' high run, but you'd better be young and fit and stay that way, and you still won't like it. If your run is any shorter than that, make sure you design in a way for you to access all of it in order to catch birds, retrieve items, clean, etc etc.
Good luck, have fun,
Pat
As far as deciding on a design to build, it will be a great deal more pleasant and non-back-breaking for you to work in if you build the run 6' tall. You *can* bend over to catch birds, rake poo, etc in a 4' high run, but you'd better be young and fit and stay that way, and you still won't like it. If your run is any shorter than that, make sure you design in a way for you to access all of it in order to catch birds, retrieve items, clean, etc etc.
Good luck, have fun,
Pat