I don't use Google Play Music myself, but I had a look at the options:
Are you using the web client, or the
unofficial desktop client(or another unofficial client)? For the web client,
there are apparently plugins available(at least for Google Chrome) to allow basic controls like play, pause, stop, and skip, through global hotkeys(the desktop client has them built in).
I really want to be able to set up my voice attack profile to choose specific lists or artists and start a radio playlist at my command.
That sort of functionality won't be possible using hotkeys of any kind. Unless there's browser plugin that allows more advanced interaction, or such functionality is integrated into the desktop client, you'll have to switch focus away from your game to interact with Google Play Music.