Hi Patti, Happy New Year!
I didn't know the answer to your question, so I tried it. No, a new reply to a topic on an archived board only brings the topic to the top of that particular archive. It does not kick that topic onto the current talk thread.
Good question, I wondered about that myself. Now we all know.
Dom
PS - By the way, the post does show up as a new post for those who use the New Postings icon/link. And of course, that particular archive would show the new postings blue dot icon on the Forums' home page. It's safe to say that such a post would not go unnoticed.