Does JavaMail support notification of new emails through server-push?
If yes, where is the documentation for that? If no, is there a library that can do it?
A Store event listens for notifications issued by your backend store:
http://java.sun.com/products/javamail/javadocs/javax/mail/event/StoreEvent.html
But in my experience the java mail docs are so thin in places, that the best way of finding out what is going on, is to debug through the process yourself.
This is a great allround resource as well; the JavaMail FAQ :
http://www.oracle.com/technetwork/java/faq-135477.html