De acordo com a esta página possibilidade está disponível no Outlook 2010:
Are either the primary or secondary Exchange accounts running in Cached Exchange Mode? If the second account is in Cached Mode, then you will see the new email notifications.
Infelizmente, esta opção não existe no Outlook 2007. Aqui está uma postagem no blog que sugere uma solução alternativa usando o VBA:
It doesn’t look or behave the same as the built-in notification, but it is functional. The solution is to use a bit of scripting to monitor the additional mailbox’s inbox, watch for new items, and display a pop-up dialog-box when it detects one. The dialog-box is a standard Windows’ dialog, not the slick-looking notification that Outlook uses. The dialog doesn’t fade in and out, nor does it offer the ability to open or delete the message as Outlook’s notification dialog does. It will steal focus and you have to click a button to make it go away.