Is it possible that a catalytic converter be defective and emit fumes only when the car is driven even if it passed smog test?

The muffler shop and the mechanic think that my 960 catalytic converter is defective and causing exhaust fumes to enter the cabin when the car is moving even if they could not find any leaks when they inspected the exhaust pipes. They believe that it is worth it to replace the catalytic converter. Is that possible? Your thoughts please.

 

sounds kind off bs but i think their should be a way to test that. maybe keep a carbon monoxide detector in your car. i think theyre only a few bucks at walmart