That scenario doesn't seem very likely. It is true that NASA Langley in Virginia was bailed the two F8U-3 prototypes for sonic boom studies after the Vought program was canceled. One arrived on 26 May 1959 and the other a month later (the latter was primarily used for spares). Flight tests were accomplished through October 1959 (I don't know the date of the last flight) and both airplanes stricken a month later.
It is also true that there were F4Hs at Pax River during that time, No. 6 from 27 July to 13 August 1959 for NPE II, initial carrier suitability evaluation, and No. 3 in October, also likely for a couple of weeks, for NPE III, autopilot and air-to-air refueling evaluation. And Pax River and NASA Langley are not all that far apart.
However, No. 6 probably didn't leave the NAS Patuxent traffic pattern much, if at all, except on the ferry flight from St. Louis and the one to return.
I don't know whether there was any overlap between No. 3's visit to Pax in October and NASA's F8U-3 flight status; it's likely that there was and possible that they did tangle at least once.
However, NASA test pilot Donald Mallick flew some of the Langley F8U-3 flights as described in his autobiography (a pdf can be downloaded for free from this NASA website: www.nasa.gov/centers/dryden/history/Publications/index.html).
In any event, given the relatively brief periods of overlap of the two types in the area and the intensive and controlled nature of the flight-test programs involved, it seems very unlikely that there was much opportunity for mock dogfighting. One of the two pilots would have had to have enough fuel after completing the test points on his flight card to go looking to bounce another fighter in his vicinity that turned out to be an F8U-3/F4H that happened to be airborne at the same time.