Yes, cargo boxes do reduce gas mileage. Anything that adds weight to your vehicle -- including cargo and additional passengers -- makes it so that your vehicle needs to expend more energy to move. This means that fuel consumption is increased and gas mileage is decreased. Additionally, the presence of a cargo box on your car's roof makes it less aerodynamic and the added wind resistance will lower your gas mileage. Even the sleekest cargo boxes will have an effect on your overall fuel consumption.