currently no onsite private messaging interface and notification, these are sent to the email and not everyone has a mobile android, iphone etc with push notifications of new emails.
making the person no know if have a private message if not check your email, so it would be possible to:
when people type a private message to another user and click on send private message event is captured by the plugin, and in the widget appears: you have 1 private message please check your email
perhaps someone with experience in q2a plugins (like Noahy, scorch) could provide it in benefit of the community.
its possible? thanks