To amplify on this correct answer- the passenger and the baggage can fly on different aircraft, but only if this is the result of airline operations and not a specific request of the passenger. The reasoning behind this should be readily apparent.
Not completely accurate.
To clarify, if you are going to standby for an earlier flight, your checked bags will go on the earlier flight regardless of whether you make that flight or not.
However, the OP is traveling on an international itinerary and AA technically does not allow standby for an earlier flight for an international itinerary.
If the OP's IB flight to MAD is departing from the AA concourse, and assuming the flight to ORD is on time, the bags should make it.