I personally would, but I've done some experimenting to see what worked for me. I have 2 binders, and one is a little looser that I wear if I know I'm going to be doing something active. Put on your binder and go for a jog or bike ride, or go play basketball or something. See how you feel and how much it affects or breathing and movement, and then decide from there if you want to wear it for gym class.
Everyone is different, and just because other guys here say they can or can't run in a binder doesn't mean it will be the same for you.