Short answer 'Nope"
For future reference, when it's BLM land if Open camping, no RSVPs.. FCFS (First Come, First Serve) and typically BLM is free for 14-days then have to move a certain number of miles away, ~28 mi or like that. But NO Reservations. Some BLMs have improvements like a BBQ, Fire Pit and Shade canopy and charge ~$5
Hope that helps...
There are no reservations for this area but i do not think it would ever fill up. Remember, driving into Wedge Overlook is a washboard road and at one point very challenging for any vehicle of length as the road peaks up and curves. I was in a 28 ft Class C.