Have done it but not with a hammock. I think it's doable with some stealth camping involved...and being ready to go to ground if you have to. No doubt you could hang at a lot of the designated sites, you'll just have to plan your overnight stops accordingly....and get to them early enough to get the pick of spots at the sites. Check to all the resources on the nps.gov site for MRNP...lots of good info buried in that site. This link http://www.nps.gov/mora/planyourvisi...trailmap-2.pdf
will show you the number of spots available at each site. Some of the best camps (Indian Bar and Golden Lakes) have quite a few spots but get packed quick. Recommend you move fast too. The reservations opened up on March 15th and it can get competitive if you're looking for a peak time of the season.
I'll be giving the Northern Loop Trail a try with my hammock in August. Can't wait!