The new runway is indeed a taxiway conversion. However, it is not there for parallel ops. This taxiway is still being worked on at the moment, but once it is fully strengthened, it will become Auckland's runway, while the present runway is resealed. This interim runway will make for some nice close take-offs!
On the subject of a true parallel runway, AIAL has recently recieved consent to build a second runway, to the north of the current one. However, it would be somewhat shorter - more than likely it would only handle domestic traffic and the odd transtasman 767.
Hope this clears things up
"So powerful is the light of unity that it can illuminate the whole earth." - Bahá'u'lláh