My T does. All throughout the session she's writing, but not in a distracting way, it's just something I've noticed (but mind you I've been seeing her for years). Also she keeps the flow going and there are very rarely pauses so she can write something. Usually it's pretty short things like bullet points or maybe a sentence or two.

The T I saw at my college didn't write notes during the session which was weird for me because I had gotten used to my home T who like I said always writes notes.

My pdoc does notes at the end of the appointment, sort of at the same time she's doing scripts.