I'm no emissions expert, but this is my understanding of a smog pump:
It basically just pumps fresh air into your exhaust pipe to help dilute the emissions that get measured on the other end. There's a couple of vacuum operated valves that have some sensors somewhere that control the amount of air pushed to the exhaust. I'm sure all the CA guys have a good handle on emissions.
. Ask them for a better explaination.
It won't hurt anything if you leave it hooked to your offroad pipe. You can take it off or leave it on. Be sure to take your belt off and check that it turns freely by hand. Had a buddy replacing a harmonic balancer recently and when he had the belt off, he found that his smog pump was so bound up that it could barely be turned by hand.