My husband's in the military and we've moved a bunch of times, so have been in plenty of base lodgings over the past decade or so. I have never, ever, ever met anyone staying there who wasn't connected to the base in some way. Civilians (other than family) can stay if they are base or gov't employees there on official business, as can military retirees if there is room available, but I've certainly never heard of regular civilians using the base lodgings. Now, with the security situation as it is, I'd highly doubt that you'd be able to get onto the base - some places even I can't, as a military spouse.
Anyway, they're more expensive than hostels, and tend to be isolated with not great transportation (no public buses, trains etc. stop nearby) so I don't think there would be many benefits for the non-military traveller.