It should work, at least it does with Ableton Live. If you mean BSP being master clock and the DAW being slave, that would. You actually wouldn't use the BSP clock out, because that's for analog clock, but you can easily send MIDI clock and transport data through MIDI or USB to your computer. Then you just have to set your DAW to accept incoming MIDI data on given port. I did this for some time for triggering drums from my PC with the BSP sequencing them, but I got so tired of computers that I've ditched it and bought a hardware sampler.
Edit: Tempo and transport (play, stop, record, etc.) should be fine but sequence length won't work since it's not standard MIDI data.