One possible way:
1. Capture this event with defining onkeypress attribute
2. Detect that ENTER is pressed.
3. Invoke Ajax request for this form using a4j:function
4. Return false to avoid non-Ajax request
In general, this question is pretty popular. Search in Google for submit form enter keywords for details
Why define an a4j:function instead of just having it call the a4j:commandButton's click function? I guess I was just a little suprised in general that I have to explicitly click the commandButton to get an ajax request.