If I get a message in my IN -box on my Facebook account, can I also expect to get an e-mail notification to my registered email address?

If so, how long might it take to get that notification?

Depending on your email notification settings (http://www.facebook.com/editaccount.php?notifications), you may or may not receive a notification of a new message on facebook.

I believe the emails are sent out as soon as the activity occurs, so you should receive it very soon.