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It shouldnt. Connect a DC Amp Meter in series with the negative battery cable and see what your BCM Sleep current draw is. It should be 20 milliamps. If its high, pull the power wire off the changer and see if the current drops.
When you turn the key to off, the BOSE Amp and system should shutdown. The CD Changer has a HOT at ALL TIMES power wire. It is also monitered by the serial data line and the BCM should shut it down if its working correctly.
If the BOSE relay is stuck on, that may be your issue. The realy supplies power to the AMPLIFIERS and is mini relay#43 in the instrument fuse panel