You can authorize your Soldiers to go the gym as long as it does not violate any orders you have been given by your superiors. If you allow a Soldier to go to the gym because your mission is complete, that is your call.
It is important to understand that you are responsible for your decisions. If a superior wants to know where someone is and you tell them you sent them to the gym, be prepared for their response. It could be okay or it could be a significant emotional event. Either way, you made the call, you keep the responsibility. If you want to be proactive (and I suggest you do), contact your supervisor prior to making your decision on the gym trip.