To summarise the answer - no it doesn't. Turn up any later than 60 mins though and you may not end up flying. What airport and service you're flying also matters.

I often turn up at WLG for TT flights normally 60 mins out. If I'm checking a bag it's normally 10 - 15 mins tops to get from kerbside to Koru. This gives 15-20 mins to have a feed before boarding starts.

If I was flying out of AKL longhaul there is no way I'd even contemplate such timeframes due to everything just being bigger. I've arrived in AKL on slightly delayed domestic connections and walked into international terminal with just under 60 mins before departure and with queues at immigration and screening found myself at the gate 30 mins before departure with the entire plane basically boarded.