Yes 100%
It would promote further forum activity, help keep the forums active, people will easily know when someone has replied, quoted or tagged them in a post and would help people keep track of threads they have replied on and replies to that post.
1. Notification system which when quoted or have a new reply to your thread you get a alert this could also link with the subscription system so you get a alert when a thread you have subscribed to receives a new reply.
2. Mention Me - Tagging. Get a alert every time someone uses "@username" in a post.
This would be great but would require a whole plugin to be coded due to looking into this, there is not a plugin available for the forum software in use which covers these features.