I have traveled that road often on a motorcycle and have observed other motorhomes on it. It should be noted that is not recommended for commercial trucks. It has numerous switchbacks and a couple of genuine hairpin turns. Guess it depends on the size of your MH and how comfortable you feel.
We took that road with our 33' Class A a few years ago. Slow and easy, no problem. That Tow/Haul button is your friend, use it for hills like that, both up and down. That will save riding your brakes, overheating them.
Bad decisions make great stories!
Made it to Cherokee NC but didn't drive the coach through the park on 441. decided to drive around the park on Interstate 40 just to lower any stress. Drove the Mini cooper through the park yesterday to Gatlinburg and had a blast. Love that car.