It seems like an OK idea, with two flaws:

1. Sending people email is annoying.  
   Part of what I like about Stack Exchange is the only email I get is the stuff I sign up for - when sites start sending me "reminder" messages I get cranky and tell procmail to do unseemly things to their messages.

2. The Stack Exchange inbox is a great place for this, unless the user never comes back to the network.  
   The kinds of users who don't accept answers will probably be hit-and-run users ("I got my problem solved, why come back and bother with that whole *participation* thing?!"), so the notification icon won't ever bother them if they don't see it.  
   >The converse to this is that people who have a question migrated somewhere and forget about it but *are* active on other sites will see the notification, so this one may be a wash...