The O2 sensors and back pressure have absolutely nothing to do with each other
The O2 sensor simply measure the relative O2 content in the exhaust gasses. They dont care if your cat is there or not, they will still function the same. The problem you are having is the rearward sensor is telling the ECU that the cat is not working, because in fact its not there. What people do is remove the rear O2 sensor from the pipe, but leave it plugged in. You wrap it in foil since it is heated and is a fire/burn hazard. Without going into too much detail, this tricks the ECU into thinking the cat is working. I can explain it though if anyone is curious.
Its also possible that the sensor(s) is bad. Do you know for sure what the code is for that check engine light? If it is the cat (or lack of one) the code description will be "catalyst system efficiency below threshold (bank1)" or similar.