There are a couple of tight turns on the park road with somewhat low overhang.... Have to watch for those and stay in the middle of the road to keep from dragging your roof line... Lots of big trucks use the park roads getting across the mtns...
We love camping at ELKMONT CAMP inside the park with our OFF-ROAD POPUP setup... Its an easy drive going to both of the places you mentioned but we are in our truck doing this...
When we camp at Elkmont we always go to TOWNSEND for groceries and supplies... Gatlinburg and Pigeon Forge is a very very busy town both day and night haha... Driving your CLASS C through both of those towns but especially Gatlinburg will not be much fun... Gatlinburg is a walking town with folks everywhere... We always give them the right-away even when they are not at cross walks.... Also Gatlinburg will not have a easy parking for your Class C... Can't just drive up and park at a store and get out to go visit it... Pigeon Forge on the other hand is not as bad for walking folks and in most cases you can park close to the store you want to visit... At Gatlinburg I would park in one of their parking lots and walk the town just like everyone else is doing ahaha... It even gets worse when school is out - big time...
Almost all of our camper roads go through Gatlinburg TN haha... Been doing it for years and years...
Roy Ken