The smog pump does not cool off the cats. It only pushes air into the exhaust stream during cold starts to add oxgen to the rich afterstart mixture. This creates an after-burn in the cats to get them up to their operating temp where they work. Most cases where someone's cats plug up after removing the smog equipment is due to air leaks that were not sealed up properly. If you introduce a significant amount fresh air into a lit catalyst, the cat will melt down in a matter of seconds.
The smog pump robs power because it runs all of the time, even though it's only really used during a cold start. If you trace the system, you'll notice that it has two stages: The first is to light off the pup cats, then it switches from pumping air into the ehxaust ports to pumping air directly into the underfloor cat. I don't know exactly how long this lasts, but it's not continuous. The third stage just dumps the air.