Typically, the second O2 sensor is just used for emissions control. If a cat. is malfunctioning, that O2 sensor notifies the driver by a CEL that something is wrong. The second O2 sensor is not used for tuning...that is the job of the first O2 sensor, MAF, MAP, etc.
My last car came with three cats. After removing all three, of course, a CEL was triggered, but there was no loss in performance (actually there was a huge gain). Feeling less power is in your head, or your exhaust is too big, or flows too well (lost backpressure); not because the lack of a proper O2 sensor signal.
That being said, certin new cars ('03 Porsche 911 comes to mind) are programmed to go into limp mode when the second O2 sensor indicates a cat. malfunction. If that was happening in your car, you would have no power at all.