Yes. I did this on my Mac, with Reaper, and it worked easily. Simply plugging the USB cable between my computer and mixer allowed reaper to see a 24 channel in/out audio device from the CQ. I could click on a track in Reaper, click a track routing, and add say channel 1 of the CQ as a hardware output of that track. Go through and do this for each track in your DAW. Once done there, go to the CQ Config Tab and Inputs. You have to change each input from Analog (the preamp) to SDHC/USB.
Once you do this, you can click play on your DAW and all the tracks you mapped to the CQ will come through as if you had a device plugged into the XLR jack. You can mix, add FX, mess with output routing, etc.
Sorry but I don’t really understand your headphone question.