Off the top of my head I think there are several ways you could do this.
The main requirement is that you have the Ax on AC power and the Wifi turned on and connected.
There are several Push Email applications
Emoze and
Seven spring to mind but I know nothing about them.
I think Seven requires a phone.
You can use an exchange server and have the messaging application check for mail at regular intervals.
In fact I believe you can do that with Pop or Imap as well, but I may be wrong.
Windows Live can be on your today screen so that you can see any new emails at a glance.
There may be ways of setting an Audio alert as well, but I've never tried.
Personally I prefer to get my email when I want to and not have it interrupting me all the time.
That's a start for things to look into, hope it helps.