I dont know specifically for NZ. I only know for AUS. If its the same, then it would be a yes.
I know you can transfer in 1000 lots, up to 50000 per calendar year between ascent and ascent. If its anything else different, will be charged at $5 per 1000 points which i think is quite steep.
There is also a thread here somewhere, its quite recent.
BTW is that for CX or non CX but one world booking? because would be interested in your experience as it feels quite insecure to be submitting a form for availability, seems primitive to me..... otherwise i would use AM!