The US Army actually has a sportsman section called the World Class Athlete Program. At last Winter Olympics, one of the bobsledders didn't deploy with his unit so he could train/complete and wasn't sure if he was going to deploy to Afghanistan after the Olympics were over or not and do PR/promotional stuff for the Army instead (I don't remember if I ever read a followup on if he did deploy or not. EDIT: He did). The Olympic sport shooting team usually has a few team members from the Army, too, and other miscellaneous sports are represented.
Yeah, there are similar programs in all the services. I was serious when I said if we had any troops that were of Worlds caliber they'd be allowed to compete.