Upvote:0
According to NZ's baggage rules, no. You can only get Star Gold benefits, which includes an extra bag, when the itinerary includes 2 or more Star Alliance carriers.
If you are flying non-stop on NZ, you do not meet this requirement.
Upvote:1
I can't say for sure about Air NZ, but I have done this with Delta, including the award tickets. You can call them and ask them to put a different Frequent Flier number on your ticket, and then the eligibility for benefits would be defined by this number. Unless AirNZ has a requirement that you should only use your AirNZ FF# on award ticket (Delta and Alaska do not), this should be easy.
You may need to do this in advance; at least with Delta if you already got a free upgrade (which can happen up to 5 days before the flight depending on your status), they will not be able to remove the FF# from the ticket.
Note that many benefits (such as access to priority checkin, lounge and priority boarding) you can get even without having your FF number on a ticket - you just need to show your frequent flier card. Used this a lot last year, when I flew Delta while parking miles on Alaska. However free luggage allowance (and complimentary upgrades) are generally tied up to having FF# on a ticket.