Yes, you can drive on almost any road in New Zealand. We do recommend taking our Stress-Free Insurance when driving a lot on gravel roads or unsealed roads as then any damages caused by these rough roads is covered.
There are only 3 roads in New Zealand you are not allowed to drive, these are the 3 restricted roads:
Skippers Canyon Road near Queenstown
Ball Hutt Road near Mt Cook
90 Mile Beach in Northland
Also, you must not - unless authorised by us - drive or take the campervan on any road, which is temporarily/permanently closed or restricted, or on beaches through streams, dams, rivers and floodwaters.