Not currently (Novotel AKL Airport isn't yet built), although there are some that are a 5-10 minute shuttle ride away (some free, some charge for it).

Cab to downtown is approx NZ$60-70 each way. Shuttle is significantly less (if only 1 or 2 people). Airbus is $16 oneway, $23 return (less $1 if you print out the voucher from www.airbus.co.nz) - and now runs 24/7 [nb some hotels are 1-4 blocks from the nearest airbus stop]