Yes this is true.
But Alone catalytic converter can not do this. Actually A/F sensor is responsible for that, air fuel sensor is fitted in converter.
The basic function of converter is to convert the dangerous gases to safe gases or low level dangerous gases.
There are so many factors for exctra fuel consumption
Converter choked,
A/F filter bad or not working properly.
Way of driving (sudden acceleration, heavy breaks)
Over adjusted brake lather shoe.
Stuked calipers
Any bad bearings.
Not properly tuned engine and so on
I dont think that my opinion is the last.
Wait till some professionals can give you the complete opinion. Thanks