Yes. Your alternator produces higher voltage which drives your Coil packs to higher voltage. Your fuel injectors are also driven off of voltage pulses. There is a voltage offset map to compestate for the fuel injectors but it is seldom acurate.
These cars tend to have low voltage. Your 02 is def low voltage. Mine has 12.6 at idle and no more then 13.5 going down the road. This is just enough to charge the battery.
I had a WRX on the dyno once and did a test. I hooked a full size floor standing Battery charger/starter to the car and did a dyno pull. I made an additional 20whp almost across the board. I unhooked it and the power dropped down. Nobody seemed to believe me. I was searching for a way to add 1 to 1.5 volts. This is common to in the GM world. Companys make plug in voltage devices that raise the voltage for this very reason. GM owners report more power ect...
One thing you can do, Is buy a V7 or V8 JDM alternator. They are higher map rating because the JDM cars had DCCD difs and HID headlamps. They bolt right on and are a direct replacement.