I don't have instant notification of incoming e-mails, and I doubt I would ever need this option. I already file my e-mails in specific folders, if they are to be kept. I check my e-mail at certain times during the day. In other words, e-mail hasn't been too much of a time waster for me.
As far as using e-mail in a library setting, I appreciate the public library system of "Ask a Librarian" and think it could be useful in a school setting. Also, if we had access to all of our students' e-mail addresses, it would be a nice feature to send them overdue notices, reading group notices, and other library-relevant messages.