I don't know about IMAP idle, but other systems I've used basically send a SMS message to the device that tells the client (on the device) that there is a new email. This avoids the constant connectivity issue.
This is (basically) the way BES (BlackBerry Enteriprise Server), Novell's GroupWise Mobile Server, and EAS all work.
This is from Microsoft's web site:
Note: Using this systems means that there is not a constant connection to the server. The SMS basically "wakes up" the client to go get the new information.
An event is generated in a user's Exchange account when a new message arrives. This event causes a Short Message Service (SMS) notification to be sent to the user's device. The device synchronizes in the background. The user data is updated to the most current information, with no intervention on the part of the user.
The notification is sent as an SMS control message to the device. It is different from a regular SMS notification, because it does not appear as an SMS message in the Inbox. The SMS router and Exchange ActiveSync on the device process the notification. The notification itself does not carry any sensitive data.
Notifications can be sent from Exchange Server 2003 directly to the SMS address of the device, or through an aggregator (for example, a corporate service provider) configured by the Exchange administrator. For notifications to be sent to the SMS address of the device, the administrator must create an SMTP carrier in Exchange System Manager.