No, once your ship leaves port, even if you're cruising New Zealand waters, you’re no longer covered for hospital or medical expenses by publicly funded healthcare or your private health care provider, meaning they won't cover any expenses incurred on-board the ship.
If your cruise is in New Zealand waters, you would need to select a Comprehensive policy with Cruise Pack add-on, choosing the New Zealand Cruise region. This includes the benefits of an overseas policy (including medical) as well as the benefits of the Cruise Pack.