I've been to the Mountain Bridge Wilderness Area several times with no problems. Caesar's Head S.P. and Jones Gap S.P. mainly. I told them I was hammocking and that I'd probably be around the edges of the designated sites instead of in the dished area in the center...he said I should try to stay within the actual confines of the site b/c "LNT means LNT," but that as long as I was being responsible they wouldn't do anything about it.
Here's my trip report for one of the Jones Gap trips:
I also hammocked for the Foothills Trail thru-hike with no problems.
Trip report: http://www.tothewoods.net/FTDay1.html