The P0420 code typically indicates an issue with the catalytic converter efficiency, but it doesn't always mean the catalytic converter itself is faulty. It could indeed be related to the oxygen sensor in the exhaust system.
Here are a few possibilities:
Catalytic Converter:
The catalytic converter may be failing or not operating at peak efficiency, which triggers the P0420 code. This could be due to age, damage, or contamination.
Oxygen Sensor:
The oxygen sensor, specifically the downstream sensor (often referred to as the "rear" or "post-cat" sensor), might be malfunctioning or providing inaccurate readings. This can falsely trigger a P0420 code.
Exhaust Leaks:
Leaks in the exhaust system before the catalytic converter can also cause this code. It allows air to enter the exhaust stream, throwing off the readings of the oxygen sensors.
Engine Misfire:
Persistent misfires can damage the catalytic converter over time and cause it to fail.
Given the mileage and the fact that the car runs well, it's not uncommon for the catalytic converter to still be in good condition, but it's still essential to diagnose the issue properly.
Regarding your question about whether the computer logs when the check engine light comes on with the corresponding odometer reading, it depends on the specific system in your car. Many modern cars do log this information, but you might need diagnostic equipment to access it. If you're unsure, consulting with a mechanic or dealership service center would be the best course of action. They can read the stored trouble codes and retrieve any other relevant information from the vehicle's computer.