OSMC RC: audio bluetooth using hifiberry versus hdmi


Looking for opinions:

For audio, I’m connecting OSMC to Bose Soundlink Mini via the HDMI audio out from the monitor (audio lead 3mm jack).
The sound is very good. That little Bose box is a bit of an optical illusion - it’s hard to
believe the sound coming out of such a little device.

I’m planning to swap the 3mm jack audio cable with a little Bluetooth transmitter.
So the HDMI audio out to the BT transmitter will be a short audio cable (3mm jack),
and then the sound will be sent with Bluetooth to the Bose Soundlink Mini.

My question:
If I install hifiberry USB DAC, will the sound quality be better…?
Bearing in mind that it will be transmitted over Bluetooth (so I expect some of that
hifi quality is probably lost in that transmission)

Anyone any experience with this …?