it is the most beautiful of all the rail-trails I've done.
Stealthing is a non issue. A lot of the trail goes through national forest if I'm not mistaken; and there are so many places along the route from White Top to Damascus that you can dissapear into it is moot at best.
The climb up is not that bad; if you have time consider riding up and then riding back down to your hang site....better yet start in Abingdon and go to Damascus first day and beyond to find you hang site then go up to Whitetop.
The 17 mile ride down is fun though and it's true you'll barely have to pedal
Speaking of the AT, you can hide your bike at the Creeper/AT junction and hike in as far as you want and stealth there.
Also, along the way you'll see many impromtu sites that are not stealth at all that people have used for many years if you want company.