Isso depende se você estiver executando seu cliente do Outlook no modo em cache do Exchange ou não.
Modo Cache do Exchange: O Outlook deve estar aberto para que o envio atrasado ocorra na hora designada.
Modo on-line: O Outlook pode ser fechado (e o PC pode ser desligado) e o envio atrasado ainda funcionará - ele é armazenado e enviado pelo servidor do Exchange.
"This is expected. The problem is that (in cached mode) if the message were to be pushed to the Exchange server you would no longer be able to re-edit it or stop it from being sent without restarting Outlook in online mode. Since many people set up a rule to delay sending all messages by a few minutes (to prevent that "Oh dang! I didn't mean to send that yet!" mistake), we decided that the behavior you're experiencing was the preferred one. If you leave Outlook running, though, it will send the message at the proper time".
-- Jeff Stephenson (Outlook Development)