Indeed they do. There was talk of them being based in New Zealand for exercises owing to relatively unobstructed airspace, this one photographed at RNZAF Base Ohakea, but the deal fell through.
I do like the P-3. I did a heavy maintenance check on this aircraft many years ago. It'll be retired within the next few years as the RNZAF receive its first P-8 Poseidons.
A bit of info on these two jets; 888, or 154909 suffered a ditching in May 1979 from the carrier HMAS Melbourne and 887, or 154908 was sold to the RNZAF and became A-4K NZ6214, which was sold to Draken Aviation after the NZDF retired its strike aircraft in 2001 after a period in storage outside at RNZAF Base Woodbourne. It still flies in the United States.
An air-to-air top front view of a U.S. Air Force F-16 Fighting Falcon aircraft in preparation for refueling, taken from a KC-135 Stratotanker aircraft, 4 September 1981, during a flight from March Air Force Base, California, to Hickam Air Force Base, Hawaii.