Jabbs, the Ideal Gas Law doesn't tell the whole story as there is additional heat energy when the Jet A1 burns. It's been a while since I studied chemistry but my impression was that Avogadro's Law P1V1/T1=P2V2/T2 was only true for a closed system.
Anyway...
Turbocharging an engine doesn't change the compression ratio. The compression ration is the ratio of cylinder volume at bottom of stoke to volume at top of stroke, is it not? Turbo or supercharging does increase total pressure in the cylinder, is that what you meant?
I always thought that turbocharging increases the mass flow of air (oxygen) through the cylinder which allows more fuel to be converted to mechanical energy.