If you have an archive profile, you can add stories to your "Currently Reading" section of the archive profile. You would not need to expose your email.
If the author maintains a posting on the "Promote a Story" thread here, you can follow that posting, and elect to receive email notices when the posting is updated. That would require forum registration, but your email would remain private.
If the author posts notifications on Twitter or Live Journal or some other venue, they often make note of that in their profile, or in a forum posting. You can elect to follow the author on that venue to receive updates.
At this point, we don't have a function that would allow for notification from AFF when a story is updated, and not being the coder, I can't tell you if that's even possible. However, if it is in the works, we'll post announcements as we always do--in the Site Announcements and News posts on the forum and in the archive.