No; there are (currently) not any standard notifications generated on errors.
Endpoints that support an error-channel (and pollers) can be wired up to a notification-publishing-channel-adapter to generate a notification.
However, there are no such hooks available for the Imap Idle adapter.
I agree it would be useful to generate JMX notifications for such errors; feel free to open up an 'Improvement' JIRA issue.
Gary P. Russell
Spring Integration Team
SpringSource, a division of VMware