If they are active duty members then you should be able to send them to the local clinic on base for free. If they are contractors, they should have physicals in hand when they show up to work as part of the contract requirement. It's like a contractor providing us a vehicle. We wouldn't have to buy tires in order to use the vehicle. Same principle applies.
Now if there is no access to US. government medical services, then you can pay for active duty member physicals with the permission of the Level 3 APC (Agency Program Coordinator). If the contractor cannot provide physicals then I would ask for some consideration (cost reduction) if we have to pay for physicals for their employees.
So can you use the GPC for physicals? The short answer is yes, with GPC or local contracting authority approval. Please refer to your agencys credit card guidance that identifies use of the card and specific items that are prohibited.