Have and carry in plain sight, yes. Carry concealed, no.
There are currently no statutory prohibitions on ownership of knives in North Carolina except for that now very rare novelty item, the ballistic knife. NC Code § 14-269 only regulations the concealed carry of certain weapons, including most knives except for an "ordinary pocket knife," which refers to regular folders. This exception does not include knives that are "opened by a throwing, explosive, or spring action." The "throwing" term was specifically added to address balisongs.
http://www.ncga.state.nc.us/EnactedLegislation/Statutes/HTML/BySection/Chapter_14/GS_14-269.html