Yes having a bad idle air control valve can affect your vehicles gas mileage.
The idle air control valves job is to control the idle speed according to the computer and when you first start your vehicle the engine is supposed to idle at a higher RPM for a minute or two and then the idle speed is supposed to drop after the engine warms up.
If the idle air control valve does not work properly and doesn't lower the idle speed then your fuel consumption will go up.
One of the most common symptom of a bad idle air control valve is irregular idle speed and high engine RPM that doesn't go back down.
Vacuum leaks can also cause a high engine RPM or increase in fuel consumption.
It would be a good idea to get the vehicle checked out to see if the idle air control valve is going bad or is bad or if there is a vacuum leak somewhere.