This would go in the recent activity page.
This makes perfect sense. I would also possibly suggest one of those orange bar notifications on the fly, but I know how much you hate those.
Edit I should clarify that I am talking about the orange bar notifications for things like badges that appear on the top of the screen, not the idiot envelop flashy thing.
Problem with the notifications bars is that you do not see them unless you're on the effected Stack Exchange site. My suggestion would be to add an "alert" type to the existing "comment" and "answer" types in the inbox list. The first time a user clicks an alert, give them the option to opt-out of getting the alert messages across all sites, or from a list of the sites.