Well, depending on what happened with Canada NORAD might have been a bit less of a factor than you might think.
I'd also imagine that SAC was assumed to have been involved simply going by the continued survival of humanity and the fact that things in places like Nevada, California, and DC survived.
The defensive strategy for a nuclear war more or less being to put as many planes up in the air as possible to shoot down incoming missles, while submarines (arguably even more effective) do the same with their own guided missles, and any orbital defenses we have rain down "Brilliant Pebbles" or whatever you want to call them, if they even exist.
All told we did pretty well when you get down to it. The #1 Target in the US (The Pentagon) is more or less structurally intact.
It's also possible that given the Enclave's air support that they have control of what is left of the SAC. They probably have more than Vertibirds, but honestly fighter jets and such are of limited use for what they are doing.
Since, Canada was annexed and America was a lone gigantic superpower, we seemed to act without our allies by the time of the Resource Wars and took Canada without much of a fight, I very much doubt there ever was any integration within NORAD between Canada and the United States like in our timeline.
The argument that was originally used to build NORAD, a central headquarters in which all the branches of the military takes orders from in the event there is an assault on North America excluding Mexico, with the level of complication and sophistication that would be entailed in controlling a massive war machine like the United States had would make that argument all the more stronger.
The North Bay complex would act instead of NORAD for the Canadians. It would have been interesting for both to have survived and are trying to move out from their respective facilities, but of course, sure they survived, they probably wouldn't have had the amenities and necessities to survive.
The Enclave wouldn't have had control over, if they couldn't get control over Vault 101, I doubt the survivalists who would be left inside NORAD would give themselves over to some odd organization claiming to be the "New" United States. The Enclave, anyways, was headquartered on their oil derrick in the WEST, never NORAD, and then in Raven Rock in the East so I doubt very much the lore would support their control of NORAD. All the Enclave has ever used or has had at their disposal has been Vertibirds.