Blacksheep :
If I understand you correctly, you're saying that BlackIce uses Messenger (not the online chat tool, the network message tool provided with Windows for donkeys years) to alert you of problems and that if you stop that to avoid popups you'll lose notification of potential intrusions.
You should be able to configure the firewall to stop incoming traffic to the Messenger service port - stopping inbound NetBIOS and broadcast UDP traffic should do the trick - while keeping the Messenger service active for programs on your PC (like BlackIce) which use Messenger to provide notification.
A quick search through C&I over the past few weeks for "Messenger" comes up with a few threads which then have links to all sorts of useful stuff.