I've just done that because I forgot the hassles in LA. Yes, you have to go through customs and immigration and collect your luggage, then turn round and check in again (don't waste any time!), and you have to apply for an ESTA authorisation online, on which you point out that you're in transit to Auckland. I doubt that they turn back people who are in transit, though.
Air NZ also fly via Hong Kong, which I would have booked if I'd remembered - could you do so? Much less hassle, though flying east always seems more disruptive.