As a once and future car nut, the idea of electric superchargers have been around for a while. What I'd like to see is how an electric supercharger is better than a mechanical supercharger other than more fine grained control over the motor.

For the non motor heads:

Turbo: exhaust spins a compressor which shoves more air into the engine producing more power.

Supercharger: a pulley running off the engines main drive spins a compressor which shoves more air into the engine producing more power.

Electric Supercharger: electricity powers a compressor which shoves more air into the engine, producing more power.

One of the main reasons electric superchargers haven't really caught on is that power to spin the supercharger has to come from the alternator which itself derives its power from the engine. So in essence, a mechanical supercharger does the same job but it cuts out the alternator as the middle man. Granted, I tend to think in terms of what will generate the most HP and torque for the least cost so suppose with the right programming and fine tuning the ECM and the electric supercharger, one could achieve excellent fuel mileage which seems to be their goal.