Don't think so. There are campsites on either side of it a ways up/down the trail, but not really right there at the building. They have the hostel there, and don't really encourage tent camping. I think you'd be happiest around the Springer to Three Forks hiking area - and seeing Long Creek Falls, the cemetery, and maybe beyond there. If you have time to hike on to Neel Gap do that. . . otherwise, drive over there. Also - there are cabins for rent right at Neel Gap, so you could call and get the numbers (several different cabin rental agencies) because in Oct. it's likely to be reservation only. Several hiking trails out from the cabins to different water falls not on the AT.

You might also be interested in the Hiker Hostel in Dahlonega as a place to stay before/after your hike. (hikerhostel.com) They also would shuttle you to/from your hike.