I can confirm this as my car is wired such that the 12v is always on so the player never switches off but stay's in standby mode. This is how it is wired from the factory as I just swapped the standard connectors from the original factory fit hifi to the Empeg.
Yesterday I went to use the car for the first time in a week and the battery was as dead as a dodo.

As a question does the 'Power Off' item on the menu actually switch the Empeg off or does it leave it in standby mode?

Ray