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.
Another method of being fair to moderators is to mutually agree to delete your comments yourselves, and not have to rely on flagging at all. This can be a little tedious, but I've done it in the past (though I can't recall ever initiating it myself), and it works.
Perhaps the best method of deleting obsolete comments, if there are a lot of them, would be to flag the whole post, and leave a custom message that says something like "I think all the comments here are obsolete."