I'm completely amazed at this thread - I have actually been asked the
exact same question as the OP poses several times in the past. And,
as many times as I've been asked, I still haven't heard a real answer
to my reply:
"If it's important enough to be notified that you have new mail, why
do you insist that Outlook be closed at all, aren't you going to open
it anyway? And isn't new mail notification already a function of
Outlook?"
I'm bookmarking this one, maybe I'll get my answers - oddly enough,
the people that have asked me in the past if it's possible could never
answer my return questions...
Exactly. Which brings up your earlier question - why not just leave Outlook
open? If you don't like it in your taskbar, then you can configure it to
minimize to the notification area (or system tray). Search help with the
word "Minimize."