In my experience with P0420, this is what happens:
1. ECU logs a pending code if the problem occurs once. This CAN send it into default mode, but often does not.
2. If P0420 occurs during several more driving cycles, the CEL is illuminated and P0420 is logged as a trouble code. Car is still in default.
3. If you continue to drive with the CEL on, eventually it will turn off. P0420 will be stored, and the car will return to normal. Lean burn will once again become available, as will auto stop and all regular functions.
I don't know off hand if the cycle will repeat eventually, as I have gotten into the (bad) habit of just resetting the code. This gets me 100 miles or so before it comes back, or sometimes longer depending on how long it takes for the readiness codes to be set.