Acho que o recurso do qual você está falando se chama IMAP-IDLE e de acordo com o lista de wikipedia , o Outlook é capaz de IMAP-IDLE.
O IMAP-IDLE notifica um cliente de email conectado sobre novos emails recebidos. O cliente de e-mail conectado pode, então, recuperar / buscar o e-mail.
O principal artigo wikipedia do IMAP explica ainda mais a diferença entre IMAP-IDLE e 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).