Removing Air pump affect on O2
 

I'm looking for someone, hopefully a mechanic, or someone who really knows, hopefully has experience with what I am wanting to do.
I have an '81 with the smog feces still intact. Initially, I want to disconnect the smog crap and cat convert, but leave the ECM and fuel delivery in place.
If you disconnect the air pump, and no air is injected into the exhaust manifolds at each port, I would think that the lack of that injected air would result in the O2 reading richer at the exhaust. Presently, when the air pump injects air into the exhaust exiting the cylinders, that should result in a leaner reading because you have added air to the burnt mixture from the exhaust. Presently, with that leaner reading, doesn't the O2 tell the ECM to feed more of a rich mixture?
If I disconnect the Air pump and remove the air injection manifold that feeds the air to the ports of the exhaust, won't that lack of air injection cause the O2 to read a richer mixture, resulting in the ECM sending a leaner feed to the carb?
Isn't the O2 just a measuring device with the ECM determining how much fuel to send to the carb for the 14.7:1 ratio? Wouldn't the O2 send whatever (rich or lean) to the ECM and then the ECM adjust the mixture to the carb?
I guess I am asking if I just pull the smog crap, will the O2 and ECM send a good mixture to the carb, or will the carb also need some adjustments, and if so, what adjustments?
If that makes sense????

Honestly I think it's either an all-or-nothing proposition with respect to the emission controls. I think you'd just be getting into a real nest of snakes to try to do what you're proposing.

Yeah, that's pretty much what I think too. I put mine to sleep for the winter, so I won't get to this until the spring.
I think I have a bearing going in the air pump, so will probably have to pull it. I just didn't really want to do the whole enchilada until something went wrong with the ECM, Carb or dist.
Thx for the input.