Are you talking dry camping in one of the forest service campgrounds, or dispersed camping at the gravel road pulloffs? Boondocking does not mean the same thing to all folks. If you haven't scoped out the dispersed sites before you go I'd echo what Huachuca says and try one of the campground first. This also gives you the option of asking someone for help if you have questions.
From what I've seen, most folks with onboard generators run them for a couple hours in the morning and again for a couple around dinner time. Pisgah's campgrounds allow 4 hours of generator time a day between 8am and 8pm, as long as you are in a generator allowed loop, at least that's what recreation.gov states.