I think your misconception may be the Drivers and how they work.
Your remark "What I wasn't sure about is whether the audio signal, as generated by the DAC in the interface ..."

The VSTi's and DXi's get installed in the computer and the ASIO drivers handle them there.

Some drivers may force you to send the audio back to the USB device (via USB) afterwards and then be available in the audio outputs there, which is why I thought maybe some adapters may work or be needed. I know my Focusrite 2i2 has very little routing possibilities (no mixer software in the computer).

I have never researched ASIO drivers that will feed Bluetooth.
Then again, I never use Bluetooth .. though the Bluetooth speakers I have seen usually have a little 1/8" audio input available (for phones and such).

Make your sound your own!
.. I do not work here, but the benefits are still awesome