Nope, it injects O2 to supply the needed component for converting the bad gasses into good gases. The two reactions that happen are:
CO + O2 --> CO2
HC + O2 --> H2O
So basically it reduces carbon monoxide and hydrocarbon emissions by converting them to carbon dioxide (what we exhale) and water.
Thanks for clearing that up
Then, I wonder why the tube from the air pump connects to the x-pipe after the cats?

Seems like it would only be adding air to the exhaust after its been catalyzed.
Edit:
Ok, after some research I found that I am partially right about the crossover tube.
"Changing function
As emission control strategies grew more sophisticated and effective, the amount of unburned and partially-burned fuel in the exhaust stream shrank, and particularly when the catalytic converter was introduced, the function of secondary air injection shifted. Rather than being a primary emission control device, the secondary air injection system was adapted to support the efficient function of the catalytic converter. The original air injection point became known as the upstream injection point. When the engine is cold, air injected at this point cleans up the extra-rich exhaust and raises the temperature of the exhaust so as to bring the catalytic converter to operating temperature quickly. Once the engine is warm, air is injected to the downstream location — the catalytic converter itself — to assist with catalysis of unburned hydrocarbons and carbon monoxide."
Source:
Secondary air injection - Wikipedia, the free encyclopedia
It is used as a secondary system to quickly heat up the cats during cold startup.
Once the engine reaches a certain temp the primary system takes over and diverts air to the cats below.
So, what I said about just eliminating the crossover tube would allow the emission system to FUNCTION.
I suppose it would just take longer for the cats to come up to temp without it.