This depends on the email hosting service you setup
if your domain comes with hosting that includes email accounts then most likely yes - ask your provider for the settings
if your domain does not come with any hosting then no it wont by default - you can sign up for a google apps account which allows you to have what looks like a gmail account just with your own domain - follow the instructions over at google apps - google does support microsoft outlook - i would recommend using the IMAP service over the POP3 service because you then keep a backup of your email in the cloud
EDIT
i just reread your question,
Short answer is no you cant, long answer there is a possible workaround (if your domain host supports it) is to forward email from your .co.zw domain to your outlook.com email address