Correct, jraef.
Answer to original question: it depends on which kWh you are asking about. Load kWh or metered kWh. It makes no difference whether you put the question in terms of kWh or kW.
Increasing the power factor toward unity has no effect on the real power requirements of the load. There may be some secondary effects that reduce the kWh slightly, but there are no direct effects.
However, it is true, as others have pointed out, that all current, even reactive, contributes to copper loss behind the meter. You are heating your wires more, therefore paying more, with a low power factor than with a high pf.
William