Yes indeed. 2 wheels or 4, just go slow. I'm telling you it is rocky as all get out but only problem. I saw several tent campers there. For a street bike you will certainly want to keep your feet down. Lol
It depends on several factors; type of bike, type of tires, weight, etc. I rode all over the area on my KLR650 with Dot knobbies but I wouldn't try it on a Goldwing. It's typical desert sandy, rocky, etc.
I have camped where it is easy for a street bike to camp in fact one time a fellow drove in at the camp past mine and pitched a tent for the night. Some of the roads in are rougher you will just have to pick which interests you. I always go in at the farthest south camping area.