These are surely not purely client-side XMPP... clients, though? In order for you to receive push notifications, some server somewhere is connecting as you in order to relay the messages through GCM.
No need for a relay. The actual XMPP servers nowadays support GCM natively. The client generates a GCM token and just hands that to the XMPP server. The server doesn't have to send actual message content either, it can just be a "wake up, there's a new message" ping the app can handle specially.
Even if you send the wake up. You can't open an xmpp connection in the background
There is an XMPP standard for asking your own server to send "new message" pings via a GCM proxy. Nothing has to "connect as you".