I think so.
Leaving around obsolete comments clutters the page, and these comments are no longer useful.
What might be a good practice, in case you're worried about the fact that "author's thanks is now dangling," you should flag that comment as "obsolete," because that comment no longer serves a purpose, either.
If you want to maintain a record of why certain edits were made, you can write that into the edit summary.
....although, to be fair to moderators, you should consider leaving your comment there as proof that the OP's response is truly obsolete, because viewing half a comment conversation can make it confusing to moderators, unless the only comment left is a "Thanks! Edited that into the post," which is very clearly obsolete.