You can, and I've even seen people stay on the same bus as it does the full circuit airport to city to airport.

Here is a rough timeline. Obviously could get lucky and breeze through (I've gotten landside in 5 minutes from gate before).

1320 a/c arrives at gate - assume on time
1335 get to immigration, assuming not in first or business class
1415 clear immigration, assuming not on Australia/NZ passport
1430 clear customs
1435 clear quarantine x-ray
1500 next bus departs
1600ish arrive in central city (depending on where you want to get off)
1620 take next bus back to airport
1730 arrive back at airport (grrr rush hour)
1740 get exemption sticker from bank
1800 clear immigration, assuming not *G or in business class (if *G or business class then use the NZ premium check in lobby for a shorter queue)
1810 arrive at lounge, assume not spending ages shopping duty free
1830 boarding is called

So very little time to spend in the city itself.