I'm using Outlook 2003 but I'll mention something that seems relevant. If I open Tools, Options, and click on the button named Junk E-mail, the Options tab of that panel has a checkbox for "Permanently delete suspected junk e-mail instead of moving it to the Junk E-mail folder". I haven't tested how enabling that feature affects Outlook's behavior but I'm wondering whether it would stop Outlook from putting notification in the tray. Seems logical but, again, I haven't tested it.