Non-Apple chat services with iOS Messages (iOS Messages feature request)

A great feature with Messages on OS X Mountain Lion and the Messages app on iOS makes it possible to receive messages on both devices. This makes it possible to leave a chat at the desktop/laptop computer and continue it on the go with the iPhone without interruption.

With Messages for OS X Mountain Lion, it is also possible to register GMail (as well as IAM, Yahoo and Jabber) accounts in order to have all GMail/Google Talk chat contacts right within Messages on the Mac.

However, on iOS the Messages app does not recognize any registered GMail account (registered in the Mail, Contacts and Calendar settings) as also being a Google Talk account, and so it is not currently possible to leave a Google Talk chat in Messages on the Mac and continue it on the go with the iPhone Messages app.

I think it would be a very nice addition to the iOS Messages app if you could have Google Talk messages being pushed out to it (and even possibly other protocols that are currently supported by Messages on the Mac).