We made that exact run thru the Smokies down thru Columbia SC summer of 2013. It was a gorgeous ride with ZERO difficulties. As others have mentioned, keep your speed down and use Tow\Haul. You will enjoy the heck outa that trip. Btw, a few real cool tunnels to go through too. They are real tall so no worries.
2010 Cedar Creek 5th Wheel 34SATS "The Beast"
2006 Ford F350 Lariat 6.0L Diesel
2003 Harley Heritage Softail "Hogzilla"
1988 Harley Softail Custom "The Fireman"
1986 Marriage to "Wifey" (patience of a saint)