The oxygen sensor mounts on the header right? If there is no cat on the car and just a straight pipe through, does this cause the oxygen sensor to malfunction? Will the absense of a cat affect the running of the car or performance? I'm speaking purely ECU-wise.

The cat is downstream of the sensor, so how could it detect anything? Other than the smell of your exhaust, i don't think not having a cat would harm anything.

The Smog ***** on this site will have fun with this one!!

before the ****'s come get me, hear me out, this under a completely hypothetical circumstance!

There is no O2 after the cat. Therefore there will be no O2 code.