Sure, as long as you don't actually want to email someone else. AWS, DigitalOcean, Linode, anywhere you might want to host your email server, they're likely already blocked by all the spam filters so you're never going to get through.
>You can't host your own Facebook page.
You can't host your own Gmail either, but you can host something awfully similar to Facebook while not being exactly Facebook.
If you host something "awfully similar to Facebook" you can't communicate with Facebook users. If you host your own emails, you can still communicate with Gmail users. Surely you weren't intending that retort as a serious argument?
Gmail is just the webinterface to Googles mail, I can host the latter, while using the former with a proper client.