[Arran]

Have you opened up that plug? It may be that the third wire is connected to that brass stud on the side of the plug and has nothing to do with the electrical outlet. Philco probably used this odd combination cord because the set is in a chairside style cabinet, and it was deemed a cleaner setup as opposed to running a separate antenna wire. You could probably replace it with some appliance cord, I see flat three conductor cords all the time on electric kettles, and waffle irons, etc. Would it pick up noise? Probably, with all of the switch mode stuff around today. When I first read your post I was thinking that some sets used one side of the power line as an antenna coupled through a capacitor, but usually on early FM radios, they didn't have that third wire. A lot of old intercoms ran the signal through the power cord, and to the next unit through the house wiring.
Regards
Arran