Does it rely on a local SharePoint Group with enabled directory services with AD, meaning that the SharePoint Group creates a mail distribution list which SharePoint manages? Or is it managed by an email enabled AD group?
It depends on the specific usage on course. E.g. if a SharePoint group in entered in the Mail to field in SPLMS reports then it takes email of each particular user. If any of the group members don’t have an email they won't get this report notification.
That’s almost the only example of where you can set sending notification to a group.
Else if a notification is meant for sending to a specific user (e.g. course completion notification) and he doesn’t have an email, there is no checking to find groups where he is member and send the notification to another address. He won’t get a notification in this case.
I believe SharePoint alerts don’t allow to select a SharePoint group.