Mic's vs Un-mic'd? No. The room - the music - the balance of what I'm hearing - constantly effects it. But mic'd or not doesn't really play into it.
I agree with room, music, balance, etc 100%, but disagree on reinforced or not being of no / little consideration. Some kit elements translate well unmic’d, but some do not, especially the bass drum in lower dynamic sections. For example, if I’m feathering or in a section using grace notes on the bass drum, my approach varies considerably between mic’s & no mic's. Still very much influenced by the more important factors you mention, but mic context really factors in, especially relating to the low end delivery experienced by the audience.
I get in a perfect world all systems & engineers would strive for realistic representation of the stage sound, but, at least in my world, that’s rarely the case, leaving me to adjust around them. Judging my internal dynamics is so much easier un-mic'd for sure, but regrettably, outside of a rehearsal setting, that’s a maybe once or twice a year experience these days.