You can check in at any time. However, they do not have to give you a site assignment until 1pm the day of your scheduled check-in.
Example: Arrival date 7/1. You get there at 2am on 7/1 and go to the check-in desk. They will check you in, give you a phone number to call later, tell you when you may call that number for your site assignment and they may or may not let you stay in the guest parking lot until you get your site assignment. Your best bet if think you'll be arriving in the wee hours of the morning of your check in date is to either stay at another campground or hotel when you arrive, get some shut eye, and go to the Fort around 7am to check in. At that time you will get no hassles about being parked in the guest lot, you can enjoy breakfast at one of the resorts or other restaurants in the area, go to a park, call the # around 1pm for your site assignment, and come back to set up.
On very rare occasions when the Fort is not too busy, they will give you your site assignment early in the morning and let you check in and set up at that time. It's kind of a crap shoot.