No experience but seems there is a bit of road riding involved once you hit the flats in case that isn't your thing.
This page shows each section and some make note that bikers are allowed, so I'd assume the ones that do not state it do not allow biking (like the first section, on the AT).
http://www.ncmst.org/mstsections.htmlI'd suggest sending them a note to ask?
kdixon@ncmst.org