I have been looking at this as I have recently setup IMAP mail in OS X Mountain Lion Server
I referenced this Apple document...
which shows that the mechanism for what is loosely classified as 'push' is different for OS X & iOS. OS X Mail uses the IMAP IDLE function (if it has been enabled in Apple Mail) whereas mobile devices (iOS = iPhone & iPad) use Apple Push Notification Service.
IMAP IDLE keeps a communication link between the IMAP server and Mail on OS X, therefore for both notification of new emails and read status the notification is immediate.
For the Apple Push Notification Service I suspect that it only notifies of new emails, it does not update read status until the clien mail application is opened and the client communicates with the IMAP server.
I tested this by having running — Apple Mail on OS X + iPhone + iPad. From another machine on the LAN I sent three emails. All three devices registered each new email arriving (the iPad actually I have to 'wake up' sometimes?!).
On the iPhone then I opened one of the emails — the unread count went down immediately on the Mac, on the iPad no change. Then I opened mail on the iPad, the unread count adjusted. I then opened the second email — the unread count went down immediately on the Mac, on the iPhone no change.
From this I deduce that Apple Push Notification Service does not have the same full functionality as IMAP IDLE and only notifies of new incoming emails.