There are two routes in. Exit 20 off I-40 to Cove Creek Road is the only one I'd take a trailer on.
We've camped there a dozen or so times, the past few years with a Scamp 19' and Tacoma. As mentioned by others, a 3-4 mile section of the road is dirt, winding and narrow. Oddly enough, it goes back to two lane paved once you get into the valley.
Its fairly common to see trailers as large or larger than yours in the campground and at least one set of hosts has a good sized "A" but it really boils down to how comfortable you feel in situations like this. There are definitely no places to turn around from the time you hit dirt until you reach the valley.
With or without the camper, give a couple of warning horn 'beeps' when approaching a blind curve.
Cataloochee is a great campground with plentiful wildlife. We've never been without spotting several Elk