Well, you can record and recall everything about CQ, at a given time, by saving it as a scene. However, just about everything gets saved and recalled with the scene so you can’t really see a plot of volume levels or recall very specific things about the scene. You aren’t going to be able to apply DAW like automation on the CQ where it’s continuously riding a fader/pan/etc throughout playback of a song and I’m not totally clear what the use case would be for something like that. However, you can create scenes like virtually every other digital board so that you can recall “points in time” across the mixer as a whole like for the beginning of a song, bridge, etc.
Not sure if I really answered your question but, as I thought about it more, I was thinking you wanted DAW like automation where all sorts of sends, pans, and faders are being automatically adjusted throughout the timeline of a given song. I’m 99.5% sure that isn’t possible on the CQ and I’m not personally aware of what board it would be possible on or how it would be used in a live setting.
Take care