There are no client-originated persistent connections (i.e. a listening socket) on AppEngine, so it's quite impossible to implement a real-time push system on it.
As you already know, you can get close with Channels API (solving push to browsers) and mobile device-specific push systems (GCM and APNS).
If you want a universal system, I'd recommend a socket based system, much like PubNub. You should look into Compute Engine which allows for such functionality.