I think the feature you are talking about is called IMAP-IDLE and according to the wikipedia list, Outlook is capable of IMAP-IDLE.
IMAP-IDLE notifies a connected mail client of new incoming mail. The Connected mail client can then retrieve/fetch the mail.
The main IMAP wikipedia article explains further the difference between IMAP-IDLE and IMAP-PUSH:
IMAP4 clients need to maintain a TCP/IP connection to the IMAP server
in order to be notified of the arrival of new mail. Notification of
mail arrival is done through in-band signaling, which contributes to
the complexity of client-side IMAP protocol handling somewhat. A
private proposal, push IMAP, would extend IMAP to implement push
e-mail by sending the entire message instead of just a notification.
However, push IMAP has not been generally accepted and current IETF
work has addressed the problem in other ways (see the Lemonade Profile
for more information).