I did a TN/NC trip last year at the end of march and it was one of the best for me! As for Tellico camping, if you want to run the river a couple of days in a row, camping out there is good, and the little river in the smokies is close by too. When I was there I looked at the camp sites, and they would be fine for boaters. No services, and minimalist campgrounds, but you are right there next to the river. Good class III stuff downstream and fun III/IV at the ledges. I would call the tellico ranger office to get the details on the camp sites. Here is some info for them.
Tellico Ranger Office, U.S. Forest Service, 250 Ranger Station Road, Tellico Plains, TN 37385. Phone (423) 253-2520.
The tellico and the little are close by, but the other NC runs are pretty far away, you might want to pack up shop and head over there for the wilson, doe, watauga runs etc.
Of course its all rain dependent, so its hit or miss. I lucked out and march is usually a good time. If nothing is going, there is always the chattooga, which is a bit of a drive, but worth it if nothing else is running. Have fun!