Sorry to ruin the idea but it isn't quite as simple as that, I have tried it.
The big problem is that email isn't stored in tables of a db so you can't connect aware up to the email system. Email is stored in folders, not db tables. The MySQL db is used to store contacts, accounts and other info but not the actual email.
If you wanted to test this yourself, I recommend iRedMail as a full open source email system, quite easy to set up, runs on Linux, and the new Roundcube web mail interface is very pretty. You can connect aware into a few things that are stored in then db but mail itself isn't one.
There is one exception to this and that's DBMAil.org it is an email system that uses an SQL db to store the mail. I haven't tried it so can't vouch for it.
If you really want to try and tightly integrate email with your aware app, I suggest you look at things like:
Mailgun, which provides mailboxes for web apps and would allow you to push mail into your aware apps.
and context.io which is a really powerful api to access and play around with imap mailboxes.
Context.io is really a very cool tool, I think you will need a plugin for aware to use it but if you had this types of functionality you can do some great things with email and your aware app. Plus you don't need to actually rebuild the email system in aware.... Which I think you would struggle to do nicely, for example imagine your TO field, there is no way to create this in aware using ref attributes that isn't clunky
If anyone has got context.io working in aware I would very much like to hear from you, so please chime in here.