Well, having posted in a somewhat cack handed manner, I have been taken behind the bike sheds and spoken to...
Seriously though, it is a question you may be asked, and many "airport authorities" (which is not ATC), and these airport authorities now have specific orders for specific situations such as the one here.
We often "standby" for the military, just in case the aircraft can't get into their own nearby bases, however, its very unlikely that we would accept a diversion for a military aircraft who had u/c problems, no other emergency, and sufficiant fuel to make it to their own base or a nearby one.
That mindset applies to many airport authorities when it comes to civilian aircraft, regardless of the size, due to the potential damage that could be caused.
Although, if you declared a Pan with u/c problems, I wouldn't think twice about doing whatever I could to help you, and to hell with the airport authorities opinion....