Hi Mike,
No, not really. It was an F-18 digitally CGI "skinned" in post production to simulate an F-14. For non flying ground shots, they used the F-14 static display aircraft off of the Midway Museum in San Diego.

Same exercise for the Lockheed DarkStar and enemy MiG aircraft. F-18's actually flew the maneuvers with appropriate CGI "skins" added in post production.

The shots of the various actors in flight were in the backset of F-18F's, with Navy pilots "up front". The four aft facing digital camera set up was tested at Pax River NAS for any digital interference with the F-18 controls. The cameras allowed the wide angle views without the "fisheye" distortion by having them face different axis direction angles and digitally melding the various cameras together.

A really good book by one of the pilots who flew many of the aerial maneuvers and also in the front seats with Tom Cruise is Frank Weisser's "Lead Solo: Learning Life's Vectors from an F/A-18 Blue Angel Aviator". Weisser flew as solo with the Blue Angels twice, with a few years interval in between. He flew both the "DarkStar" takeoff sequence, as well as the extremely low level run, stirring up dust across the desert