I have done some more research and testing on this and Elliot's link confirms that IMAP IDLE is not supported on the iPhone. Therefore, setting up an IMAP account on the iPhone will fetch email on a schedule or manually.
However, as Bill pointed out if you setup an Exchange (i.e. ActiveSync) account then email is "pushed" if you desire. I've got it working on my iPhone and it's really cool

The more I play with Zimbra and learn how to configure and manage an email server..the more I likey
