I'm not sure that your phone will work for emergencies. You might want to check with Verizon, or check your phone specifications. Ideally you want a phone that can connect to 900 MHz 2G. That is predominant through the islands. 2100 MHz 3G is available in some areas. If your phone can't connect to either, it won't work for any calling anywhere in FP that I am aware of.
IIRC I had to pay for Wifi even as a Plat AMB when I stayed at the IC properties in Tahiti and Moorea. But, as a spire hopefully you can get it for free.