Clarification- the AIR system does not recirculate exhaust gas. (That's EGR)
When the engine is cold, it injects fresh air into the exhaust system to provide surplus oxygen, which is used to burn up the cold/rich mixture and heat up the cats to operating temperature faster. It reduces emissions by burning off the excess hydrocarbons during this rich running condition, essentially.
Once the engine (and cats) have warmed up the system shuts off.
Since the AIR system doesn't run when warm, and you're unlikely to do a smog test with a cold engine, there should be no impact to measured emissions whether the AIR is even present or not. Only a visual inspection may cause you problems (assuming anyone remembers what it's even supposed to look like!) or if the computer throws a code if it detects the pump wasn't running (maybe in 96 with OBD II, this happens? Not sure.)