On Drupal Answers, there are many 1-reputation users with an unregistered account who write a comment, or a different question as answer. The fact they don't see an "add comment" link, and they see a text area where they can start to write, doesn't probably help.
I understand that not showing immediately a text area where to write an answer could probably be a wall for new users (although I think it would be clear what the purpose of an "Add your answer" button is), and I am not going to suggest that. I think that showing an "add comment" link that shows a dialog box explaining why the user cannot add a comment, and that comments written an answeras answers are going to be deleted could probably help.
The link could also be disabled, and show a tooltip explaining to the users why it is disabled. That is what is done on meta sites when users cannot edit (or suggest edits for) posts written by other users:
