Do musicians (or just composers?) think in music?

Yes... well, sorta!

I've done a lot of harmonic analysis in my *day(s) and because of it, as I listen to a song, I (often) catch myself thinking about what the (diatonic) function of each chord is as it is being played. It is a skill originally developed to make it easy(er) to transcribe music, but often turns what was conceived as form into a function... not that those are in any way, shape or *form mutually exclusive, but.