um... if vertibirds flew on oil, why did they make a huge mushroom cloud when they went kaboom!?
They don't fly on oil. Like most other prewar vehicles, they're fusion powered. Just like the Highwayman in FO2, or all the exploding cars in FO3.
Oil is an extremely valuable resource even if you don't burn it for fuel, since it's used to produce plastics.
As for how that relates to the NCR and any potential air force - it kinda depends on the NCR's level of technical development. That is, whether the NCR has redeveloped the ability to produce small scale fusion plants or not. If so, we could easily see aircraft. Probably Vertibird-style tilt rotors. If not, probably not, since there's no other effective fuel around.
'Course, if the NCR has small-scale fusion plants, they're halfway towards making their own PA too. Since PA production is considered voodoo magic by everyone but the Enclave and possibly the Midwestern Brotherhood, I'm not sure how I feel about this.