I am from New Zealand and have a 7 hour stop over in Guangzhou Baiyun Airport.

Yes, you can. But you have to apply for a stay permit at the airport first. You need to complete the "embarkation/disembarkation card", together with your travel documents, boarding pass for the onward connecting flight and travel itinerary, go to the inspection counter of China Immigration Inspection to apply for 24h stay permit.