AIS question

Guys, I'm curious about something to do with the AIS. I understand it is there for two reasons, one to mix fresh oxygen with any unburnt fuel to help it ignite in the exhaust to burn off as much hydrocarbon as possible, and secondly to fool emissions into thinking the exhaust is cleaner.
But here's my question, since the AIS pump is pumping fresh air into the exhaust and with the oxygen sensors downstream, will that cause the ecu to burn slightly richer during the closed loop rpm cycle? Because the oxygen sensors would be picking up on the more oxygen rich exhaust.