Kurt is correct, the air pump/smog system is not necessary for the cats. Running without it will NOT ruin your cats.
However, the part where people screw up is when they disconnect the system and don't plug it off properly (ex. weld up the air tube to the H-pipe and plug off the holes at the back of the cylinder heads). If you leave leaks in the exahust system upstream of the cats, raw O2 will get into the exhaust, the cats will over-temp at high enginesloads, and the bricks will melt down. (The beest case when thsi happens is that the cat will just melt into itself and plug up, the worst case is that the molten cat will reaspirate into the head and wreck your engine, but that's more of a concern with modern close-coupled cats and V6's.)