In reference to helicopters as not being air force assets, that's not entirely true. Both the Irish Air Corps, and the Rhodesian Air Force, had helos, which are under the AF.
Even the USAF, uses helicopters though in a support role. That being said, it wouldn't be too far fetched to see the Enclave claiming an old AFB, as it would definitely have a larger surplus of parts etc.
An interesting point to chew on....is the Vertibird an Army, Navy, Air Force or Marine Corps asset?
I'm assuming its an Army asset, but that is based only on the fact that we've only ever seen the Enclave's Land Forces, and of course there is anecdotal evidence that supports a Naval branch as well.
from the Drill Sargent's Dialoge file, it suggests that Navarro at the least was a Army installation;
Don't have any? You expect me to believe that, maggot? The truth is you lost an expensive piece of army-issue equipment. That suit is going to come out of your pay, and you will remain in this mans army until you are five hundred and ten years old, which is the number of years it will take for you to pay for a Mark II Powered Combat Armor you have lost! Report to the armory and have a new suit issued to you, then report back to me, private! Dismissed
Here's what we do know about their organisation:
http://fallout.wikia.com/wiki/Enclave_Armed_Forces