Looks like an awesome ride.  If you go, be sure to go a few days early to include a ride on the Bryson City train, and a raft trip down the Nantahala river.
 
We lived in the Carolina's 20 some years.  The mountains are spectacular as is the coast.  In between are the convoluted Piedmonts which are a series of hills with steep 100' tall rollers.  My guess is you'll climb 10,000 feet just through the Piedmonts.
 
Wish I had the time off, I might consider it.