So you can actually die and fail "finishing" the game after placing the third artifact while getting shot by the final boss. Doing this will not get you to the credits and will just restart the bossfight. Under the current ruleset this is totally fine as all you have to do is place the third artifact. Just wanted to ask this question before starting to run the game.

yes, that is correct. time ends as soon as you place the third artifact, so any death after is irrelevant.