I doubt it increases security
The spooks will be sniffing the wires between the sender and your email server. STARTTLS is a rather poor solution, which a lot of major email providers don't support, and which a MiTM can trivially short circuit after which the connection will still proceed, unencrypted for easy sniffing.
Plus it only helps for sending/receiving emails from others who the spooks can't get to. That's not the case for the vast majority of them, so if you email someone at aol.com, gmail.com, hotmail.com or so forth they'll just get your email on the other end.
You have to encrypt the body of the email if you want to be assured of security, but at that point it doesn't matter whether you run your own email server or not.