It is "curvy", but it's all good road. While I've not done it in our RV, it should not be a problem for you in your 34' rig. There will be a number of 180 degree switchbacks, just be mindful of traffic and you should be good.
I would avoid 19 between Cherokee and 40, however, in your motorhome. Drop down to 74 (the Smokey Mountain Expressway). Still very scenic but 4 lanes, no white knuckle sections.
Jay & Peggy Monroe with Dolly
Can't take it with you - don't plan on leaving any behind
2016 Newmar London Aire 4553, Spartan chassis
Wrangler Unlimited toad