I grew up near that area (Franklin, NC). We have run the road many times all thru the year. It is a beautiful ride. Watch out for the bears as they will run across the road right in front of you. And don't feed them, they are very dangerous as most have lost their fear of humans.
You need to be very, very, very comfortable with driving your RV down very narrow, curvy roads with very heavy traffic. The summer traffic, especially on weekends is bad. Take your towed instead. It is a shame to miss such beautiful scenery and you would be limited as to where you can pull over in an RV. Plus there's lots of idiot drivers on that road.
If "I" were staying in Gatlinburg (not that I would) and just was popping over the Gap to stay at another campground in Cherokee or Bryson City (not that I would). I would drive it. But I would do so very early in the morning before the tourists get started (although the fog is quite bad as you climb up towards the Gap). But I learned to drive on roads worse than 441 thru the Park. But it's the tourists that are the biggest problem. It's hard to drive when 1) you've never enountered a curve in the road before and 2) you are trying to look at the scenery, scream at the kids in the back seat and try to talk on your cell phone all at the same time. I've seen it done and there is almost no cellphone service on that road (so who are they talking to??). Watch out for the few semi's that run it. They eat up both sides of the roads and you had better move over for them, no matter what you are driving.
As a local and someone who loves the GSMNP, drive your RV down I-40 and take 441 in your car! It is a beautiful ride. We often packed a picnic lunch and "day-tripped" for that road.
The Cherohalla Skyway
between Robbinsville NC & Tellico Plains TN is also another great drive. Ever bit as beautifull as Hwy 441 but less visited.