I worry that running a mail server will confuse users. The use case is a website for connecting qualified "sensitivity readers" to authors. A good example of a similar service is here:

http://writeinthemargins.org/sensitivity-readers/

(although we will be funded through a government program and not charge either party). Note that they have deleted the google docs spreadsheet that they referred to as a "database". I suspect that having the real name and direct email address for their professional readers publicly available did not end well for them :)

If we have a setup such as you describe, it would accept sending to email addresses outside the "local" domain and then users would get bounce messages (silently failing would be just as bad). I need users to immediately see on login that this is not "normal" email. They should only be able to send messages to the users that they have been "connected" to as part of the application process.