Install Boxcar on your iPhone. Create a Boxcar forwarding email address. After you created it, add the Boxcar forwarding email address in your GMail Settings under "Forwarding and POP/IMAP".
In your GMail Settings create an new filter. Under the search criteria "Has the words" enter "in:important". Test your new filter by clicking "Test Search". If you get your shown your messages from the Priority inbox, then the filter works.
Now under the "Create a Filter" tab check "Forward it to" to the Boxcar forwarding email address. Now you should get push notification from Priority inbox.
NOTICE: I can't assure you that this will work since I didn't try it.