A good condition and properly working catalytic converter shouldn't lower your gas mileage and in fact a good properly working catalytic converter should improve your gas mileage.
Now if a catalytic converter becomes bad or clogged up and then restricts the engines air flow through the exhaust then yes a bad catalytic converter can decrease your gas mileage.
So if you're getting bad gas mileage and you've replaced every other component for a tune up and the gas mileage still hasn't improved then you should have your catalytic converter replaced.
In some states you could just remove the catalytic converter if you can't afford to replace it.