All NFA weapons are allowed in North Carolina. Certain NFA weapons do fall under the "Weapons of Mass Death and Destruction" clause in the North Carolina Code such as machine guns. The respective statututory sections are 14-409, and 14-288.8. For those weapons that are included in this clause, one needs to obtain a permit from your county Sheriff. According to NC Code, there are strict guidelines for individuals that wish to posess these "Weapons of Mass Death and Destruction". In a nutshell, you must either need to posess them for your occupation (Law Enforcement/Military) or need to posess them for scientific study. The only other way the Sheriff will issue the permit is if you are a licensed FFL. A common way to get the permits is the FFL route. I know of several folks that got their C&R FFL and use that to get the needed permits for posessing "Weapons of Mass Death and Destruction". The C&R FFL is only $30 bucks to renew so it is not a bad deal. Bottom line is it is possible, you just have to jump through a few extra hoops to do it.
If you need to see how the code is written go to this website:
http://www.titleii.com/BardwellOLD/nfa_faq.txt
Hope this info helps.
Dan