The transmission would be hell... gearing it high enough to produce usable boost (compressor RPM) would cause either terrible lag at low speeds or compressor stall/overboost at high speeds, unless I'm mistaken..
If it's geared to produce maximum boost at 10-14000rpm, you'd essentially have no boost below that and would otherwise be wasting engine power just spinning it (as a conventional supercharger) therefor proving to be completley counter-productive in an F1 engine...
OR
You gear it so that you have maximum boost in the low revs (6-10000rpm) and then run into stall or overboosting at high revs.
Just how I see the situation...