Yup, but I don't think it is possible. The webaccess would have to poll the mailbox every minute or two to check if any mail has arrived. Gmail and other such mail systems reflect the number of new/unread mails in the browser tab. The client does a similar thing in the Windows Taskbar.
We don't have notify for WebAccess in 2012 or in Windermere for that matter. However, in Windermere we do now autorefresh WebAccess. It's not exactly Notify but it's a step forward. I believe having a true Notify is something we've got on the roadmap for a future update after Windermere.