My hunch is that it will not. Besides being well off the beaten track, it has no water, I've never seen more than a few spots being used, and often when I've driven thru it's completely empty.
In the event that you can't find a spot, there is another camping area at the end of the road, about 20 miles further north. The road is rough, so it will take you about 45 minutes to get there. It's nowhere near as desirable as Grandview, but does have pit toilets, but again - no water.
