I think you have to look at your goals to determine whether or not that makes sense. If your goal is simply to put meat on the table, then shoot the first deer you see regardless of sex or size. Now obviously that's not any type of management.

If your goal is to increase the buck to doe ration and manage the area for more mature deer then it wouldn't make much sense to shoot buttons, regardless of whether or not they get run off. Also, whose to say that those little guys that get run off won't return to the area while chasing does in later seasons?