Google has this Google Cloud Messaging info for integration with iOS
What is the difference between using Google Cloud Messaging or iOS for the same purpose?
Is
Google Cloud Messaging is originally a platform to send notification for Android. They added an iOS SDK, but using their SDK on iOS means that you are using both GCM and Apple Push notification service:
Push for iOS device => Google Cloud Messaging => Apple APNS => Device
If you are only developing an iOS app, it is best to use APNS directly. If you already have all your infrastructure set up for GCM, then you may save you a bit of code by supporting only GCM to address both iOS and Android.
However there is no specific technical benefit doing so.