I don't know but the custom is to leave something like a chair at the site to let folks know you're there but gone. There was a camp host when I stayed there and I don't think they'd book your site if you paid for it. You could always tell the camp host your plans to leave and come back.
Yes, register and pay. It's probably best to leave something at the site (like a camp chair) so there is no confusion as to whether the site is vacant.
Like others have said, once reserved, it's yours for the length of your stay. We setup once we arrived and chose our site and then headed into Canyonlands and Arches!