The Grumman C-2A which was shown bringing Gibbs and Ziva to the carrier was from the Fleet Logistics Support Squadron 30 (VRC-30) whose job is to move cargo, mail and passengers to and from carriers in the Pacific Fleet.
When McGee talks to Vance about examining the USS Seahawk's security computer mirror, Vance is in MTAC looking at a satellite view of that ship. The coordinates are 14º30.23'N, 74º58.16'W, which places it in the Carribean Sea about halfway between Columbia and Jamaica. This is consistent with where it's supposed to be in this story.
In the aerial shot of the aircraft carrier listed as "the Seahawk", you can see the name "John C. Stennis" written across the aft. The actual ship being filmed, the U.S.S. John C. Stennis is not the "Seahawk" as reported. http://www.navsource.org/archives/02/74.htm