Yes, you can! Just make sure you lower the tire pressure to 20 PSI before you do.
There is an air stations located at the Historic Corolla Park where you can inflate your tires back to specs on your way out. It is located at 1160 Village Lane, Corolla, NC 27927.
Vehicles are required to use driving lanes adjacent to the dune line between Milepost 14.5 and Milepost 17 from 9AM until 5PM beginning the Friday before Memorial Day through Labor Day. All other times, use driving lanes adjacent to the dune line or at the shoreline. Click here for more info on the Currituck visitor website.
Also, Vehicles MUST have a county-issued Beach Parking Permit properly displayed to park on the beach from the last Saturday of April through the first Saturday in October. Check out the Currituck County Beach Parking Permit website for more info.