It’s not recommended.
There are plenty of hosted email services better suited for this than Mailgun; Rackspace Email, Gmail / Google Apps, Outlook, etc.
Mailgun is meant to be a tool for developers and their applications.
Sinch Mailgun has answers! If you have any concerns or questions, please send us a Support ticket using the Support page within your Mailgun Control Panel. Our Support Team will be happy to assist!