I think it's a cool thing, and could definitely be done. I don't see why it could not simply use a, or multiple, capacitors and run off the power of the car's alternator (making more power than a regular alternator, obviously). They share the same belt in regular SC compressors, and I imagine that it would take maybe 3-5bhp to power the SC, rather than the current 10x than that, or more, it takes now.
It would really be ideal for a twincharged setup, utilizing a large turbo and small supercharger configuration. The electrical power required to spin even a twin screw type (would be ideal for this application) pushing just 4-6psi or so would not be un-doable at all, and feeding that into something along the lines of a moderately large Garrett turbo would result in linear boost progression all the way to a sky high redline, a constant minimum boost pressure which would negate pretty much every downside to turbo motors, and the engine would be extremely efficient AND produce seriously large amounts of power due to the benefit of a near zero "power cost" to drive the FI setup. I would probably run a pair of intercoolers, a small one between blowers and a large front mount post turbo, and I could see an easy 200bhp+ per liter of displacement.
Imagine a 2L I4 setup as such, making 400-450bhp from the factory, and getting 38-44mpg!
Would be very tuner friendly, as the constant boost pressure would allow a significant amount of room for tweaking the turbo and consequently shifting the power curve in either direction, faster spooling and more responsivewith less peak, or more top end with a llittle longer wait for the turbo to be making full boost.