I added a BTadapter to one of the USB ports of my Yellow Box and the adapter shows in HA, in my Iphone HA does not show up in the BT list:
You have wrong expectations, here.
Adding a bluetooth adapter will allow HA to detect and use supported BT end devices. A random example is the well-known XIAOMI Mijia Bluetooth Thermometer
HA itself does not offer any BT services, nor does it advertise itself.
Thanks so much for the clarification. What I am (was…) trying to achieve is HA to know when we are home. So, that is not possible ?
It sure is 
There is a whole domain dedicated to presence detection.
Thanks. I believe that I may have resolved this by adding my wife’s Icloud account to HA, on top of my own Icloud account. We are going for lunch now so that will show me that it works.