Google Play is running in background, but since its sandboxed it cant do anything nefarious. All Play can do is update apps. They know u have your apps downloaded, but thats it. Thats the way I understand it at least. Im assuming u can turn Off network permissions for Play Store if u want to, and then turn back On when u need to update your apps. But I dont think it makes a difference from a privacy perspective or battery drainer.