Surely it depends on the intake shape. Usually compressor intake has a diffusor (subsonic flow) that makes possible a pressure increasing before the compression stage.
I have been thinking about this and wondering me what occurs when the sound barrier is traspassed. Don't we need variable intake geometry in this case?. How is it implemented?. I have heard that compressor and turbine stages are not important in supersonic flow due to shock waves in their vanes. So that, does a supersonic jet a variable geometry in it engines?. I am not talking about scramjets (does it works subsonically?) but about combat aircrafts for instance, or the Concorde.
About the exhaust speed, is easy checking it by the momentum equation. The force exerted on the engine structure must be compensed with a variation of momentum flow. You sure be able to do this, and you will see that the force is:
F=(m(air)+m(fuel))*W - m(air)*U
where m's are the mass flow, W is the relative velocity of the gases exhausted, and U is the forward speed of the engine.
Thus, if m(air)/m(fuel)>>>1 then W>>U. By the way, it satisfies the common sense.