Since no one has yet dared to tackle the question, I’ll answer it myself.
I find that, ashamedly, I listen for the sound only a large percentage of the time.
I guess that’s the pitfall of spending a lot of time and money in this hobby.
The two are not really separable. When I listen, I put on some music that I want to hear. Often while listening I'll think, "that album sounds really good" or, "that album wasn't recorded very well" or, "they compressed the hell out of that one."
I even make note of certain aspects of the music. How does the bass sound? Do the vocals sound natural, etc? But that happens while I'm listening to the music.
I have some test CDs but I can't remember the last time I got them out. When I have it's usually to measure the bass at various frequencies with an spl meter on my phone.
I don't have a set of demonstration CDs that highlight certain aspects of the sound that I play to hear how good they sound. I guess you'd say that I notice when an album sounds good or bad frequently, but I don't listen for that specific purpose very often.