OBD2 codes will go away, depending on what the code was in the first place. Certain codes will check themselves all the time, and others are a one trip check. I am/was a Master ASE mechanic, but some people don't care if someone passes a test. I strongly believe it makes you a better tech.

Anyway, for the PCM to run the catalytic converter efficiency test(s), it first proves out all O2 sensors, four for our LS1s. Then it checks on the converters ability to store O2 for a very short period, and if it can, then the converter passes the parameter. Usually if it is a P0430, it is just that, an inefficient converter, as long as there are no other issues like exhuast leaks. I've replaced many converters for this code, usually not replacing any O2 sensors, and the light stays out. (Unless you get a cheap replacement converter, don't ask me how I know!) The downstream O2 sensor's main job is to check for proper converter operation, and the upstream O2 is mainly for fuel trim.