Yes, if it helps absolutely use the word native if that clarifies it for you. 🙂
There may well be a colloquial or cultural issue here. NZ'ers are rather protective of their (native) wildlife and about 33% of our total land mass is protected. I would say you would find it hard to get many Kiwis to regard any organism brought in by humans as belonging or being of NZ - especially considering the absolute havoc they have created with the resident (i.e. native) species.
One of the major cultural elements within the relationships between Europeans and the indigenous Maori is the concept of whenua - of the land. Like many aboriginal societies, Maori see themselves as tangata whenua: belonging to the land, rather the European-centric view of the reverse. Similarly, or as an extension of this, is a sense of custodianship of the beings that came before nga tangata whenua.
So, from a scientific or outside point of view, it might be necessary and desirable to clarify if something is native, indigenous, or endemic, by and large New Zealanders limit their association with of New Zealand, especially in terms of wildlife to the Maori nga tangata whenua. The concept of the latter is now really absorbed into the shorter tangata whenua where Maori see themselves as protectors of what came before - even if they eradicated several significant species themselves. For me, it's one of the things that makes NZ special.