Question: Does Bluetooth Output use the Audio output from the DAC Hat?

[Tim Curtis]

Bluetooth just provides the network connection between two devices. The receiving Bluetooth device which in your case is a Pi-1B configured to output to the integrated Headphone jack will output the PCM stream sent by your 3B to the Headphone jack or whatever device was configured in MPD Config.

Example

Pi-3B -> MPD -> Bluetooth Connection -> Pi-1B -> Bluez-alsa player -> Headphone jack