I don't think you can make a third party client app for any of Google's services at all. So, unless you convince Google to port their apps on your fork of Andro

I don't think you can make a third party client app for any of Google's services at all. So, unless you convince Google to port their apps on your fork of Android, your users will not be able to use an YouTube app or a Gmail app or Waze most likely. Microsoft tried to do this a long time ago for Windows Phone, and Google openly thwarted them every step of the way, changing APIs and so on to prevent those apps from actually working. And they of course refused to launch any apps of their own for WP.