ios push practicaly equals frequent requests to the servers? How iMessage push works?
About Push Notifications

As its name suggests, Apple Push Notification service (APNs) uses a push design to deliver notifications to devices and computers. A push design differs from its opposite, a pull design, in that the recipient of the notification passively listens for updates rather than actively polling for them. A push design makes possible a wide and timely dissemination of information with few of the scalability problems inherent with pull designs. APNs uses a persistent IP connection for implementing push notifications.

iMessage uses the same protocol as APNs (source), so it is pushed from the server, and does not use GSM.