It now indeed seems to be the planned path to create a full webmail service out of Mailpile. Though right now the developers still say its "written as a personal application": https://www.mailpile.is/faq/#tec-8

It's designed to run on your local machine and be accessed by your browser. You can run it on a server if you like, but the give-away is the fact that it only supports single users — the original conception was for personal use.

I heard they're moving in the direction of supporting multiple users, which will be fantastic. Then you really can use it as a proper webmail client for a small email server.