The idea behind the whole AIR system is to pump air (thus oxygen) in the cats and the back of the heads (or manifolds on the HD trucks) to help the cats start their chemical reactions faster on a cold engine. Once the engine warms up the air supply to the heads/manifolds/cats is shut off and everything pumped by the smog pumped is just being vented out into the atmosphere again. The AIR system can be safely removed from the truck, without affecting emissions testing results, provided testing is done with the engine fully warmed up (like it should be done anyways). There is a catch tho - you can remove the plumbing and the diverter valves, and you obviously plug any loose ports in the heads and manifolds and cats, but you have to leave the control solenoids plugged in their harnesses - the PCM really only cares about "seeing" them through the electrical signals it receives from them (it grounds them to trigger them), so as long as the harness is still plugged in then you can remove everything else (including the rats nest of vacuum lines) and there will be no error codes in the PCM.

Oh yes, you can only do this is counties where there are no visual emissions checks, as not having the AIR system will in many cases give you an automatic fail even tho your truck runs perfectly good and passes the actual sniffer test with flying colors...