Usually the extended warranty you purchase for your vehicle does cover the cost of a replacement catalytic converter or any other emission control device that fails during the extended warranty.
When you buy a car you get a power train warranty which is separate from the extended warranty since a power train warranty only covers parts of the car that makes the car move.
So the power train warranty would not cover the cost of the catalytic converter but if you bought an extended warranty to have extended warranty coverage then yes the catalytic converter replacement should be covered under the extended warranty.
If your catalytic converter fails then it can cause the vehicle to run rough or cause the vehicle to fail emission testing.