Both the oil burning and the defective camshaft position sensor would have hurt the CAT.
A defective camshaft position sensor can cause problems ranging from no spark combustion conditions including excessively long cranking time when starting cold, rough running, poor idle, stumbling or hesitation, mileage drop and stalling upon acceleration.
However before replacing the catalytic converter we recommend also looking into perhaps a defective rear oxygen sensor. Having leaked oil into the combustion chambers and through the exhaust system may have contaminated your Honda’s oxygen sensor. With a defective (out-of-range, weak, lazy) rear oxygen sensor your Civic’s ECU may think the CAT is damaged when in fact the sensor is not functioning properly.