Is there a way to disable the Google Play Music icon in the menu bar, while keeping Google Play Music running?
If you've already tried Command-dragging it out of the menu bar (although draggable menu itmes are a private API feature, as pointed out by comments below and usually only works with system icons like Time Machine, clock, battery, and volume), I'd recommend
Bartender (free in beta, $7 full version)
Bartender allows you full control of your menu bar by adding a second, hidden but easily accessible menu bar to organize all of your icons. Alternatively, you could request that Broomstick (free) be updated for Google Play.