Some flashes, such as my Sunpak 555, have an accessory adapter that allows the flash to be powered by AC. However, you cannot plug the flash straight into the wall. On your older flash, I think what you are seeing is just an old style synch socket of the kind used on Graflexes, Heilands, etc. It is the same thing as a two-pronged wall plug. It is simply another type of synch connector, NOT an AC connection.
Cables with these ends came in various combinations. I have two-prong to two prong male and two-prong to two-prong female (to be used as an extension cable and/or for rigging multiple flashes together), two-prong to bi-post, and two-prong to PC. I am sure there were others as well.