TRACON Controller described an event when an IFR aircraft first indicated a loss of communications followed by an emergency squawk; the reporter voicing concern regarding the supervisors decision to use another VFR aircraft to fly along side of the emergency aircraft to secure information if possible.

Narrative

Shortly after taking position; aircraft X; who was an overflight at 8;000 FT; squawked radio failure. Several attempts were made to establish communication with [the] aircraft including using the PET-2000 tuned to 121.5. For a brief period the aircraft was calling on that frequency; but had a stuck mic and was unable to hear any transmissions. At this time the Supervisor came over to my scope to help deal with the situation [and] we noticed the aircraft's mode C was no longer reporting an altitude. The aircraft was about to leave my airspace and enter West RADAR's airspace; who had already taken the hand off prior to it going NORDO. [However]; without a valid mode-C and seeing the aircraft begin turning southbound; we immediately stopped departures at ZZZ and ZZZ1 not knowing the aircraft's intentions. I also vectored aircraft Y away from this aircraft not knowing what altitude it was at. After approximately 3 minutes the aircraft began squawking emergency and very shortly after that the aircraft's transponder quit working; suggesting they had an electrical failure. We were able to track aircraft X with primary RADAR the entire time. As the aircraft started approaching ZZZ1; I was instructed by my Supervisor to attempt to have aircraft Y fly in close proximity to aircraft X in hopes he would see the aircraft and motion to the pilot to land at ZZZ1. I was hesitant to do this not knowing what the other aircraft would do or what altitude he was at; but the Supervisor was standing there watching the entire process and instructing me. The pilot never was able to see the other aircraft and I am not sure if separation was ever lost due to lack of communication and no mode C. Horizontal separation was approximately 1 mile; vertical separation unknown. As the aircraft neared ZZZ1 the Tower was able to see it and said it appeared to be lining up to land on Runway XX; however Runway YY was the active. The aircraft was still circling southwest of ZZZ1 and the Tower told me to bring aircraft Y in for Runway YY. I advised ZZZ1 that aircraft X was IFR and asked if they could provide visual separation with aircraft Y if it were to continue to Runway XX and they said they would. I then cleared aircraft Y for a visual approach to Runway YY; gave him one last traffic report; and shipped him to ZZZ1 Tower. Both aircraft continued to the airport on converging courses and arrived at opposite ends of the runway at almost the exact [same] time. ZZZ1 sent aircraft X around and I instructed them to send him westbound and that I would re-sequence the aircraft after another jet that was lining up for the runway. Weather at the time was VFR and using NORDO procedures aircraft X did exactly what was expected by continuing VFR to the nearest airport and landing. However; I am not sure having another GA aircraft attempt to fly in close proximity to another aircraft when its intentions and altitude are unknown is ever a good idea. Recommendation; if a similar situation were to occur; there should be more thought about keeping aircraft vectored away from the NORDO aircraft and not attempt to intercept the aircraft; especially with another GA aircraft.