There's such a thing as a real electric supercharger that actually produces useful boost pressure, but they need serious electricity and can only run for short bursts as a result. Anything that doesn't use heaps of power won't do any good.
I was also tempted by this idea a few years ago, so I've made a "bench test" with a
centrifugal compressor (taken from a vacuum cleaner). The power demand of the
electric motor was around 1500-1600W. According the flow rate metering, the delivered
air quantity was adequate up to the mid. RPM range for an 1.5 / 1.7 engine.
A more sophisticated compressor might give better results, but I think the power demand
would be almost the same. In a 12V system this would mean more than 80A sustained
consumption (while accelerating / or at sustained high engine loads during uphill),
and more than 110A for the spin up (at the beginning of the acceleration).