Do you know when it is coming out?
No.
Also, another idea was that I would simply hook up the emailing system of the whole website to a notification setting, ie that you would get a little notification button that shows the emails that the person has been getting?
The notification API will provide full notification handling of all forms. It'll handle sending a Private Message, an Email, or internal notification (e.g. like Facebook notifications globe). The plan is to provide this as a plugin. It ideally should replace Private Message System plugin as well as our current legacy notification API; note it'll have built in private messaging features as well and replace the email user form with one built into CB Notifications.
These API plugins aren't planned until alter of course and I've no idea when I'll get to them. I've a rather huge list of things to develop after CB Activity and GJ upgrade is done. I'll evaluate the list and order them based off importance and ease. For example smaller plugins that'll take 1-2 days will of course be done first to maximize usability.