[agurk]

And to be more detailed, in any jet turbine, the compressor blades will create power as the energy spent compressing the air will be recovered when it's exhausted out of the tailpipe. So it's not quite correct to say they will produce no thrust.

Looking at design of turbines, a lot of air is needed above the amount for combustion to help keep the post combustion chamber turbine from melting (or just weakening to the point of failure). Some of this will be the unburnt (nitrogen, etc) components of the ingested air but a lot of design goes into moving air around components to move heat away from them.

The less air needs to be compressed for the engine then the more efficiently it will run. This is often achieved by designing one that can run hotter. This is also one of the other ideas behind having the bypass on a turbofan, reducing the amount of air that is compressed.