You are correct that other things can cause the P0420 code to appear, such as the problems you mentioned.
To answer your question, since those three things have been determined to be bad, they should be replaced even if no code is present.
Another cause of a P0420 error code could be water in the gas. Sometimes simply switching to gasoline from another gas station might help, as water might have gotten into the storage tanks of the first one.
The use of high octane generally works if no other issues are present. It's misleading as to why it works, as it did for me. It could be that merely using a different gas avoids any issues with bad gas, such as water in the fuel.