A clogged catalytic converter can cause a cars engine to idle rough if it gets clogged enough.
Other symptoms of a clogged catalytic converter besides rough engine idling are, engine hesitation, poor gas mileage, failed emission testing, hard starting and even no starting of your engine.
A clogged catalytic converter creates back pressure on the engine so if the catalytic converter is clogged the engine can't exhaust itself like it's supposed to and when the engine can't expel it's exhaust from the air it intakes then the engine will have problems.
I had to have the catalytic converter replaced on my vehicle last year due to rough engine idle that no other parts could fix.
After replacing the catalytic converter the car runs great again.