[thstone]

My understanding is that the air pump and secondary air injection are emissions related, not performance related.

What seems to be happening is that there is a problem in the emissions control system and you get a CEL if you try to drive off while the air pump is still operating to avoid the CEL. You've found that if you wait until the air pump stops, then the likelihood of a CEL is much less.

The bottom line is that the emissions system needs investigation/repair. Then there will be no reason why you can't drive with the air pump operating.