I did not have a CEL light but was testing the sensor one day and there was no voltage at the wires in question. New 02 produced the same result (of course since it's the car side that was the problem). Lean burn function seems to work just dandy as do other systems. I think the 12v being there would help warm up the 02 quicker as that is it's job. However, I suspect there's only a minor change in efficiency with it not working.
Want to learn more about this. I'm going to read the FSM related to the electrical there.