Yes, but I don't see NZ ever abandoning their strategic intelligence alliance with US and UK (which produced, among other things, the original Echelon). Blowback all you want, Snowden would still be sent straight to Washington.
new zealand gave the big F U to the USA back in the 80s when they refused the USS Buchanan nuclear powered destroyer entry to the port as it violated the nuclear-free legislation.
Harbouring Snowden would probably create a lot more tension than just refusing a port entry to a specific boat, though I don't know the rest of the context of that incident.