I think there's going to be major parts of the route that are going to be dispersed only, with facilities limited to a pit toilet, if anything, to be honest.
So for example: If you're going Nobo, the first Forest Service campsite I think you'll hit is N. of SilverCity, before you hit the Work Center. It's right by the highway, and the CDT option. That's a long way, so you'll probably camp quite a bit before that.
The next campsite would probably be dispersed, either in the Gila (no facilities), or the work center (toilet, water). You could then stay near PieTown/Toasterhouse, where you could find camping at the Toasterhouse, I believe. Kinda keeps going like that. What would be your next option? Hmm: no camping until Grants (not allowed due to the National Monument?), where there's a KOA nearby, with all the fixins. Then it's probably a while to an established campground, above Cuba. A lot of people stop within the reservation to camp, but I don't have much info on that. Tons of established FS campsites in Colorado, that much is true!
A great resource would be the ACA's own maps and the new book that has come out. Long story short, I'd wager on camping without much facilities nearby, as there's plenty of opportunities, and you wanna make sure you're fairly comfortable, even if you don't make it to your hoping-for destination.
As far as wildness of the route goes - it (again) depends, but in most parts, there's a population nearby, even if you don't get that feeling from stories of being on the route - the design sort of has you avoid many towns (which is nice).
Hard to put together a summary of the conditions you'll see for such a huge route! Be pleasantly surprised, is probably a good thing to anticipate. RV's will knock you off the road near Yellow Stone, and you'll be happy to see a passing truck give a friendly, "Hello" a coupla days afterwards in the Basin.
The "Worst" camping you'll probably get would be in the back of a motel - some proprietors will allow you to camp on their motel property, in their own established places, rather than taking a room (for a reduced fee). Some places have a few rooms set up more like a backpacker's hostel with bunkbeds and things like that, for a more reduced price.
My perspective is a little skewed, I'll admit, as my mileage was many times 2x as long, and finding somewhere awesome to hang out for a spell wasn't a top priority, while racing. A little sad about that