you have to understand that the ECU of a typical modern fuel injection engine runs in two modes. Close Loop & Open Loop.
While in close loop (typically during idling or during crusing with throttle below 60%) the ecu will get the O2 sensor reading and adjust fuelling accordingly to the target of 14.7 air fuel ratio. So... no matter what fuel saving method or device you are using, the ecu will still try it's best to get 14.7 air fuel ratio in close loop. So, if you cheat or disable the stock o2 sensor, the ECU will not be able to get to the right fuel ratio.. bad for mileage and bad for the environment, or even worse you will lean your mixture so much that you eventually kill your engine. different case if you are using a full standalone management or a piggyback which can bypass the stock ECU close loop operations.
Open loop is altogether a different story, as you are accelerating at 80%-100% throttle, the ECU no longer reads from the stock 02 sensor to adjust fuel, but instead uses the ECU factory preprogrammed fuel & ignition map. that is when piggyback fuel controller comes in handy. Otherwise, change your bad driving habits, have your tyre properly inflated, and make sure your engine is in tuned. you will save more petrol that you can imagine.