TURIN:
Erm, I have to query that.
Does a prop actually compress? If so what is it's actual practical effect on the overall compression cycle?
Well, a prop blade is an airfoil, and Bernoulli tells us all about that. Static pressure is increased on the aft face of the blade. This may have little or no effect on the ENGINE cycle, but it's this pressure rise that integrates to propeller thrust i.e. the motive force for the airplane.
Granted the pressure rise is not huge, but the prop disc area is relatively large, and F=p x A. The prop moves a large mass of air at relatively low pressure.
Now if the prop has many blades and is enclosed in a shroud (i.e. a ducted fan), then the pressure rise is greater although the area may be less. This higher pressure acts to supercharge the downstream core engine.