It shouldnt the car should start but will not run correctly, will bog down, and no power on acceleration
Usually they will start just fine, as Joemom said, loss of power, no acceleration or will not go faster than 40 or 50 mph. It all depends on how badly the converter is clogged or damaged. Usually the converter is damaged while driving with the check engine light on and flashing.
So driving with the check engine light on will damage the catalytic converter
Looking for a Used Civic in your area?
CarGurus has 58,590 nationwide Civic listings starting at $1,295.
Search Honda Civic Questions
Honda Civic Experts