Ask HN: Can Dropbox be used as an email host and is it a good idea?
And this, in the context of Dropbox having Mailbox app now, is noteworthy. Don't you think?
Are you asking because someone told you it could be? Dropbox can share a static, html website, not actually be a computing machine that could run software apps like an email server.
If your question comes from a certain idea about how you might possibly do that, by all means reply and I'll see if I can explain further.