During arrival, a Boeing VC-137B-BN, USAF #58-6970, operating as Air Force 2 (AF-2), was cleared for a localizer back-course approach. At 1442:49, TRACON advised AF-2 of traffic at its 10 o'clock position at 2 mi, altitude unknown. At 1443:11, TRACON advised AF-2 the traffic had moved to its 11 o'clock position at 1-1/2 mi. AF-2 acknowledged both transmissions. At 1443:29, AF-2 advised that the flight was changing its frequency to Boeing Tower. Shortly thereafter, the aircraft commander of AF-2, seated in the right, saw the traffic, a Mooney M20C, N6507U, on a collision course. He took control and initiated evasive action. The pilot of N6507U was cruising at 2,500 ft outside the Seattle TCA and did not see AF-2, which had converged from his right rear area. The Mooney's #1 radio was inoperative and its #2 radio antenna had been vandalized, thus the pilot was not in radio contact with ATC. The last digit/wheel on his transponder was stuck on '5' and code 1205 was being transmitted. The transponder had no Mode 'C' altitude reporting capability. All of the backcourse approach was outside the TCA.