Of course it works. We've seen our users use IMAP on mobiles for a least 6 years now. But don't get so excited about it though. I've yet to see an IMAP client on a mobile that leaves a socket open (IMAP IDLE) and can get real time notifications of email arriving like you do on desktop versions. I've yet find out what impact it would have on the battery if you had the socket open all the time.
And FYI, IMAP is not push, it pushes new email notifications to the hand set. To me that is better than push. You decide exactly what emails you download to your phone and save on GPRS fees and battery power.
Most IMAP mobile clients even sophisticated ones like Profimail, are just glorified POP3 clients which have folder support. The connect download the index and then log out. If they left the socket open when you open an email you would not have the lag of opening a socket, authenticating, getting the message or index and logging out.
Another thing that is ace on IMAP on a mobile is the fact that your sent emails are stored on your sent folder on the server.
The Treo may actually have a full IMAP client that implements the IDLE command. Let us know if you can get the new mail notifications real time.