The e-ticket record will not match the pnr. At AKL check-in, the NZ agent will find no e-ticket record associated with the reserved AKL-LAX flight segment. The NZ agent would have to make an exception to allow the passenger to travel without getting a proper e-ticket issued - certainly possible.
Ideally, the e-ticket should be reissued with a new e-ticket number and a new fare calculation line. However, this is likely not possible as UA's computer system will not issue a ticket under fare basis CNZ for a codeshare flight.
Remember, a PNR is nothing. A ticket is what matters, be it a paper ticket or an e-ticket.