A catalytic converter does not reduce fuel consumption nor has anything to do with the fuel consumption of the vehicle.
However if the catalytic converter gets clogged or goes bad then it can affect the performance of the engine which could then lead to increased fuel consumption.
The main goal and job of a catalytic converter is to help clean the exhaust gases from your vehicle to make it more environmentally friendly.
Also the catalytic converter reduces the amount of nitrous oxide that is produced by the engine burning fuel.
So the catalytic converter reduces the emissions of your car which helps to keep the air in the earth cleaner than it would be without the catalytic converter.
In some states the catalytic converter must be on the vehicle to pass emissions testing and it must be in good working order.
A bad catalytic converter can cause your vehicle to fail an emission tests as well.