A recent DSLR is never completely shutted Off unless you remove the battery.
Old EOS 300D (Rebel) was really shutted Off, but when you turned On it took 2 or 3 seconds to load the firmware.
That's why more recent DSLR are not completely Off, but the consumption is extremely low as you shut Off the Power switch.
Have a Nice Day.
That may well be the case, Thierry. However, from my experience, when a Canon DSLR is switched off with the button, as opposed to being in sleep mode, there is no indication that the camera is not completely off. There's no light or LCD that may appear to be still drawing battery power, however slight.
One thing I noticed that was different about Nikon cameras when I got my D700 is that the top LCD continues to show some basic details when the camera was apparently completely switched off, such as the number of shots remaining on the memory card, or 'E' for empty if there were no card in the camera.
However, with both models, the 5D or the D700, and all other Canon DSLRs I've owned, when the cameras are switch off, the battery drain is so slight that the battery will retain its charge for several weeks or longer.
This was not the case when the Nikkor 14-24 was attached to my 5D with adapter. The battery would go flat within a couple of days if it wasn't removed. There were other oddities such as incomplete EXIF data and no reference to the F stop, which as I recall caused some problems in Photoshop when attempting to merge images to HDR, and other oddities which I now can't remember clearly.
Now I'm not sure if the sort of problems I've mentioned above are typical for most cameras that are attached to 'foreign' lenses via an adapter, but I understand there will often be at least some degree of loss of functionality.
When people are considering the purchase of a new system, I would strongly recommend they investigate the type of lenses that are available and the degree of functionality of such lenses when an adapter is required.