Tunnels on Blue Ridge Pkwy.

Yes you can. Tunnel clearances are taken 1' from the tunnel wall and increase greatly another two feet out. The parkway is one of the most relaxing drives you can take with the slow pace and no steep grades (on the parkway). Never found fuel (diesel or gas) to be any problem though there ARE a few side roads with very sharp curves and pretty steep grades so choose carefully based on knowledge. Major highways are always a safe bet.
Good luck / Skip