Depends on which way you go. If you take the first left it takes you up to Harmon's Den. Next left takes you to Max Patch. Right takes you south to Jody's ice cream spot. None of them take you back to the BRP. If it were me, I'd roll out to Max Patch, then carry on up to the river, double back to Hot Springs, and then on to Asheville. That, or run it downhill like
@cranbiz suggested, head west a few exits, come into Cataloochee from the TN side and make your way back to 276. In either case, it's tough to avoid missing a bunch of the BRP without doing a bunch of backtracking.