I have a '02 V6 (so also 1st gen), and I had to replace the secondary air pump to pass emissions a couple years back (don't remember the exact codes, but something about air/fuel; also had to replace the collapsed elbow and some solenoid). So I would expect that if you remove it, you will get codes.
I replaced the pump with whatever aftermarket part I could find. For the first 20 years, I don't remember ever hearing the pump, but now I can hear it at startup and sometimes stopping at a light. So it's doing something, but I haven't seen any mileage difference or anything. Maybe the aftermarket is just louder.