the smog pump I have does two things. pumps air into cat, pumps air into the head via an a.i.r. manifold in conjunction with the egr valve and some other devices. mil= check engine light. I know my truck gets confused if there is not "air" being pumped into the head when necessary, since the computer figures its calculations should have that air. if it does not get the air, mixture is rich o2 sensor will fault, egr will fault. check engine light then comes on, and base timing and fuel map go dumb. that is my understanding of the system at least.
I have heard that if you run a cat without the air pump it burns it up, or clogs it faster. Not sure if there is any truth to that though.
so do you have efi or no?