Note that the channel API is not supported for Java client (or iOS):
https://code.google.com/p/googleappengine/issues/detail?id=4189
Yes, you should use each platform's native push notification technology - the successor to C2DM is Google Cloud Messaging:
http://developer.android.com/google/gcm/index.html
On iOS I believe it is APNS:
http://en.wikipedia.org/wiki/Apple_Push_Notification_Service