The official app does, and has for ages. Since it was released, I think.
However, other apps, like GV Connect, etc., rely on 3rd party push apps like Boxcar.
I'm kinda stuck trying to figure out what I want to do, myself. On one had, the official app hands-down the best one. On the other hand, several of the others support TextExpander, which is hellahandy for text messaging.