JHN,
How fast do you think the turbo on you motor turns? Probably over 100,000 rpm at big boost so to get the compressor driven up to this speed you would need to have probably a 10:1 ratio between the engine crank and the compressor snout. That will typically require at least a pulley ratio and one gear set that will give you the 10:1 ratio. And if you look at it this is exactly what people like Pro-Charger are doing.
I have proposed several times on this forum that you need to mount a Pro-Charger on your engine and then the hot side of a turbo, and make it BIG, then connect a shaft between the turbine and the Pro-Charger with a sprag type over riding clutch. So the engine drives the blower but when the exhaust driven tubine gets up to speed it will start driving the blower and if it is really large it will also start driving the engine thru the blower's drive system. This is a compound engine. And remember at 60,000 rpm it only takes an additional 100 inch- pounds of torque from the turbine to make 100 hps being added to the engine crank. Now this would be efficient as you are using heat from the exhaust, which is approx 35% of the total power made by the engine, to drive both the compressor but also the engine.
Only time and money prevent me from doing this!!!
Mostly money!!
Rex