Theoretically, John is correct. In a fuel-injected engine, the mass air flow sensor will determine the amount of air flowing through the engine, and will report this back to the PCM. The PCM takes this value, and the value from the intake air temperature sensor, and determines what amount of fuel should be going into the engine (this is fine-tuned with the reading from the upstream HO2S).
Effectively, the MAF and IAT sensors handle coarse fuel trim adjustment, with the upstream HO2S handling fine fuel trim adjustment. The only way, again, theoretically, that the engine will lose mileage with a dirty air filter, is when the air filter is so plugged up, that the needed flow rate of air necessary for the engine to maintain vehicle speed can no longer be supported by the air filter.
However, poor design of the intake ducting and poor mass airflow sensor location can cause a dirty air filter to reduce mileage.
The air filter has a larger plane surface area than the cross-sectional area of the mass airflow sensor, so air always travels slowly through the air filter, and accelerates as the cross-sectional area decreases, and should be at a stable velocity before being sent through the mass airflow sensor/intake air temperature assembly. If this design element is done poorly (such that the mass airflow sensor is reading air before the velocity truly settles), then a plugged air filter will increase the velocity of the air coming through and can trick the mass airflow sensor into thinking that more air is going into the engine than there actually is, causing the engine to run slightly rich while the HO2S fights this and gets back to a proper mix. Air is incredibly fluid, so you actually get a higher velocity through the center of the tube than you do through the edges of the tube, and twists and turns change this up as well.