I can only remember the FAA doing an ILS calibration at RIAT once maybe twice.
Looking through my thousands of shots, N86, a white Challenger did a few approaches before landing and taxiing to a couple of points on the airfield to check ground equipment. It came in and departed on the 13th July, 2011, I don't think it stayed for the weekend. tbh, I can't seem to remember another visit during the show build, certainly not when the public were on base, but then again, I'm a relative newbie, having only stayed near the base for the past 14years.