The Bluetooth connection is actually a function of your computer, not DM. DM just uses the BT layer that is there.

I use a Dongle for my BT and the phone stays connected whether DM is running or not. That way you can still move files, use your laptop for hands free, use the laptop as a speaker for the phones' audio output. All these functions are independent of the DM.

As far as the on/off thing, I haven't seen anything like this.