The announcement of the schedule has timings through the end of the Northern Winter season, and then no details on how the service will operate from April to October when the US is 17 hours behind. I think we can infer, however, that NZ will aim to keep a schedule that allows for connections across to Australia on arrival. This implies actually a pretty quick turnaround time given the length of the flight and the time difference. It might be that April - October the flight arrives into Auckland slightly later, or has to leave slightly earlier to allow sufficient ground time in CHicago to turn the plane.
The relatively tight turns implied by the schedule are different than the California or even Houston service, and this will be an interesting new challenge for NZ's operations to North America.