Al, If you do not mind the slow travel you should be fine on the parkway. Others have traveled it without any problems. There are a few tunnels between Cherokee and Ashville that are a little low so you may want to check this website.
Many of the National Park Campgrounds are not big enough for the Montana but there are a lot of private ones that will be not problem. The big tour buses travel it all the time.
Hope you have a good time and trip.
http://www.nps.gov/blri/planyourvisi...el-heights.htm