I can only speak for the western part, but wild camping out in the desert should pose no problems. Water might be an issue, so you could fill up your supply in a town or rest stop, then ride outside of it, looking for a sheltered area behind a group of trees, abandoned building, or gully or wash (normally a bad idea, but winter is not the season for flash floods. Keep a weather eye out for freak subtropical El Nino storms, though.)

There are a few spots where campers congregate, though. This is somewhat off the official ACA route, but may well be worth the detour in winter: https://www.youtube.com/watch?v=i9y-...c&noredirect=1