You may get miles for SYD-CHC just as easily as you may not get miles for that leg. The answer will depend on what the W or H class on UA maps over to on NZ.

Most earnings when travelling on :-: partners relate to operating carrier earn rates. Those flights that are codeshare, operated by another :-: partner, earn as per the operating carrier earn rates. If UA W or H classes convert over to G K L S R or N classes on NZ then there will be no mileage earnt on SYD-CHC as NZ don't give miles to the partners when travel is in those classes on their operated flights.

Hope this makes sense! Too early in the morning and not enough coffees under the belt as yet.