Verified answer

If you have a faulty converter then the signals its sendig to the computer are possibly mixed messages, once you replace the converter the computer should reset & no more light problems.

You don't tell us what make/model you have, BUT

The sensor could be damaged, or not. They aren't THAT expensive, go ahead and replace it while you are under the car.

The light MAY or may NOT go off, but it will take several days at best for it to go out.

It will take that long for the computer to run the cat efficiency test again.

If you don't have a scanner or code reader, go to the local discount auto parts store and ask the nice fellows there if they will retrieve the codes for yo , and then turn the light off.

If the code they get is not a P0420, purchase a QUALITY repair manual, and perform proper diagnostics for the codes that are stored. Repair as per the trouble trees, and test again.

Let me guess, one code was for Cat efficiency and the other was for too lean or too rich at Sensor ___? This is the problem with code reading vs. a real diagnostic. The code doesn't tell you what part to replace. What you really have is a lean or rich running condition that is effecting the converter and the O2 sensor readings. The cat and sensor were probably fine. You need to figure out what is causing the car to run rich or lean.

The sensor is doing what it should do, reporting a problem with back pressure in the catalytic converter. Chances are when you do the replacement they can reset the light also.