There may not be a native solution, but Google Music All Access is available in Ubuntu 13.04 today as a web app.
Turn On Notifications
To fully enjoy the Google music experience, notifications should be present. I am only going to turn on notifications within Chrome but you may explore a more intimate integration at this webupd8 blog post.
The first step is to load Google Music using the Chrome browser. I am using the beta version 27.0.1453.81. Press the setting button located in the upper right quadrant of the browser window and select Music Labs.
Find Desktop Notifications from the list and click enable.
Add Google Music as a Web App
Although you may run this directly from the Chrome browser, the secret to an enhanced user experience is adding Google Music as a Ubuntu web app. For the details on how to accomplish this see; Ubuntu – A Replacement for Chrome OS.
Enroll In Google Music All Access
You can stream music in your library to any device or computer via a browser on which you’re signed in. You can also download music in your library to any authorized device or computer. You can authorize up to a total of ten (10) devices or computers at any one time. At this time, only two Google accounts per computer can be used to add music with the Google Play Music Manager.
Click the Try It Free for 30 Days button to begin your registration. For your awareness a list of Authorized devices will be displayed for your consideration and you will be prompted to enter credit card payment info.
Start Playing Music
Enjoy : )