The air pump is there to provide excess oxygen to the exhaust stream. It's required so that chemical reactions can continue to occur after combustion reducing controlled emissions (HC, CO and NOx). The excess O2 that's pumped in reacts with the harmful emissions turning them into more H2O, CO2 and harmles oxides of nitrogen; the catalysts speed up these reactions. The air pump doesn't just pump air to the cats (or downstream/upstream of them). It also pumps air into the exhaust ports via the crossover tube in the back of the heads. The computer triggers the thermactor valves which decide whether air gets bypassed, pumped to the heads, or into the exhaust pipes.
If you have A/C and P/S, the belt length should be around the 84.5" shown in the diagram above. But all of them are a bit different. I bought 3 - within a 1/2" on either side of the 84.5", and took back the two that didn't work. Mine took an 84". Each tensioner is a bit different, the spring gets tired and it sits in slightly different locations on each car. So just tell the parts place what you're doing and they should be happy to take back the two you don't use.