Short: It works

Long: set the phone to sleep after 1 minute on external power.
Waited for it to go to sleep.
Watched it for an additional minute as every 6 seconds or so the bt light would blink.
Called the phone from a landline.
The phone woke up, immediately showed the headset icon,
the headset beeped.
I answered with the headset button.
About 1 second of no audio and then the call was connected on the headset.

Preliminarily I would say this works

Ehud