I don't think an EDF can do that, as they don't have tremendously good static pressure, which is the one key trait a super/turbo charger needs. They do have viable electric turbos, however! They are essentially the compressor turbine and housing of a turbo, driven by a very powerful BLDC. Can make a couple PSI boost on the average engine, enough to add a kick.
Pardon the uh.. american-ness, but this does show what it can do.
On another note, I got the TVS diodes in today! I'm gonna put them into the aircraft now.