If the tax is tied to the registration, then owning an unregistered vehicle should logically not incur any tax responsibility. Certainly the 3% highway use tax would logically seem to fall into that category, since an unregistered vehicle or trailer cannot (legally) be used on the highway. Of course, applying logic to tax laws is not always successful.
If I were to go to pay tax to my state, and the state refused to take it and claimed I didn't owe it, I would generally take them at their word without too much argument. If you can find a NC DMV help line, a phone call there should help clear up the situation.