A short answer: No :-)
But with help of a plug-in you can receive e-mail into a FileMaker-database.
I'm by no way the authority on this subject, but a FM plugin might make this possible, besides a simple "No". =-)
FileMaker will not do this natively. However do not despair as there are a wealth of options when it comes to integrating email into your FM solution...
Plugins allowing you direct access to email through POP, IMAP or both:
Plugins that communicate with Email clients such as Apple Mail, Entourage, Outlook:
Setting up any of these plugins is relatively straight forward. Specifically the Dacons guys have done a good job providing very decent starter solutions...
From my experience when it comes to email, the only thing that starts causing concern is when you have to deal with thousands of emails and you need to show them through portal displays...but that is a different story all together!