I think your theory should work. The Joying is a full feature auto head unit (with a tuner, amp, etc.), but it is also a full featured android tablet with a screen that happens to be perfectly sized. As you suggest, you could connect the audio out on the Joying to the AUX in of the stock radio. The screen is detachable and is connected via a cable.
So, if you had a long enough cable, you could place the box in the glove compartment and the screen in the dash compartment. However, I think you might have enough room in the dash where the iDrive normally goes. So, you could save the glove compartment.
Whenever you wanted audio for the joying, you would just switch the radio to AUX. The screen is pretty thin and will fit in the dash compartment. I cannot detach it to show you, but I am pretty sure it will fit nicely. I have it mounted flush against the dash (given the rolled feature above the radio slot). Here is a photo from the side, if that helps.
