Does the O2 sensor being plugged in really affect the way the vehicle runs... primarily it's emissions output?

 

I am not using stock ECU so I can't say for sure, but I am pretty sure the ECU will retard the engine without a correct 02 sensor

 

The computer will also interpret the low O2 sensor signal as the exhaust containing too much oxygen, so it will make the fuel mixture really rich... something I'm fighting right now (13-15 MPG and code 25).

 

Yes. The computer uses the feedback from the O2 sensor to adjust fuel metering. While the sensor does affect emissions indirectly, the primary purpose is to allow the computer to enrich or lean the fuel mixture to allow complete combustion. Without the O2 sensor, the computer operates in open-loop mode (a warm-up and back-up mode) and a preset amount of fuel is injected rather than the amount actually needed. The engine will run rich or lean most of the time, and likely very poorly.