As new users can't comment, they sometimes posts answers that would have been comments if they could. Should we flag them so they can be cleaned up properly, or leave them alone because that's how the site works?
Yes, flag them. Answers should always answer the question.
Moderators will then either delete the answer or convert it to a comment, abusing the Answer feature for comments is not welcome.
If the 'comment' was made by the person asking the question, they should instead edit their question to include the new information. Also, the person asking the question can always comment on it, even at 1 reputation.