I haven't used it myself so not sure really how it works. From some searching around it looks like there are a couple of roundabout ways to accomplish it but not quite as seamlessly as the Messages app.

There's a couple ways to use Prowl to set up push notifications and then you would just open the GV Mobile app once you see the popup.

http://prowl.weks.net/
http://www.gvmax.com/
http://github.com/mikeyk/googlevoicenotify

To clarify: the popup won't take you directly to the GV Mobile app, you'll have to do that yourself once you see the notification. As opposed to a regular text message sent to your AT&T phone number the popup you can click Reply to go to the Messages app.