We need more data and background information. You mention the radio alone doesn't cause the observed behavior; using the CD player does cause the issue. A good IMA battery stores somewhere around 500Wh usable charge. The CD player consumes so little power in comparison (maybe 20 watts peak), that it would take dozens of hours with the engine off to notice any appreciable IMA battery drain.
FYI: The IMA battery is connected to the 12 volt system through the DCDC converter, which is located below the carpet in the trunk. The DCDC is disabled until the engine is started (i.e. turning the key to the 'ON' position doesn't enabled the DCDC, unless you first turn the key to the 'START' position). Once the car has been started, the DCDC remains enabled, even if the engine goes into autostop. However, the MCM (IMA computer) can disable the DCDC completely whenever it wants, and the ECM (engine computer) can set the voltage to either ~12 V or ~14V (the ECM cannot disable the DCDC) whenever it wants.