Adding a story to the Currently Reading list will not send a notification to you.
I don't have an update right now as to when the favorite button will be available for beta-testing. However, when we reach that stage, we'll be sure to let people know in our Site News. I would imagine, since we do have an email notification feature currently for reviews in the archive, that we would be able to implement something similar for story updates. However, since I'm not the coder, I can't say for sure.
One thing we authors can do is to use the Promote a Story thread here on the forum to announce updates. Forum members can follow that post, and receive email notifications of a new post, which would take them to the thread, and story link. It's a working alternative at this stage.