Overview
Not exactly, if what you mean is having a mailbox in our system or having Mailgun as the final destination of all your email (and then viewing the email through the UI).
Mailgun is not a mailbox provider, and we do not support POP/IMAP. The most our service could do is forward incoming email for your address somewhere else: another personal address or to a webhook.
There are plenty of hosted email services better suited for this than Mailgun such as Gmail / Google Apps, Office 365, etc.
Need Support?
Our Support Team here at Sinch Mailgun is happy to help! Reach out to us in the Support page of your Mailgun Control Panel, and we'll be with you shortly!