Does killing the priest in boss combat count against "no kill" ending?
If by no kill you mean the "not even once" achievement, than I think, the answer is yes. After a bit of reasearch, it seems to me, that this site gives the most helpful answer to your question, since someone has accidentally done it, and even after a restart still saw the consequence of it in his/her EXP. In the same site, if you open the comment section, there is a comment that states that they actually tried it on second play-through, and thanks to that didn't get the trophy.