No, they are all first-come.

The campgrounds in this area have changed from REcreation Land to the State Park system I believe. But this is what I found on the linked website for Sawmill: Jesse Owens offers four no-fee campgrounds. Campers should follow the self-registration process. Campsites may be occupied on a first-come, first-served basis with a two-week maximum stay. All other state park camping rules apply.