the propeller on a turboprop is in such a point of view also a "compressor" but its main work is to create thrust, it has very little effect on pre compressing the air which enters the inlet for combustion, regardless if its a multishaft free turbine ( eg.pt6a) or a singleshaft fixed turbine ( rr dart, tpe331 e.g ) .
when it comes again to ( 4 stroke) pistons the amount of air in the cylinder is determined on the suction cycle and the suction, as we all know it ends with the piston at bottom dead centre. the amount of air being able to suck in is describes in volumentric efficiency. - at natural aspirated engines typically below 1 , at turbocharged engines above 1 - here the engine not just sucks the air, it is forced into the cylinder. the the piston moves up again and compresses the amount that was sucked in.
so when the amount of sucked air in suction cycle stays the same a low compression engine will have the same amount of air as the high compression engine at end of the compression cycle. at the higher compression engine this amount of air is just squeezed more .
its the same when you take an airballon , put an amount of air in it and then squeeze it. sqeezing it more will rise the compression inside the ballon, not the amount of air in it ( since no further air is forced inside when you squeeze it)
cheers !