How to set up external documentation in Android Studio?

Repeating the comment from above as an answer, as requested:

Unfortunately, Android Studio has manipulated the IntelliJ settings IDE, so you cannot provide an external link in the UI to documentation. Normally the module settings (or Project Structure) would have the ability to look at all libraries and configure where to find external docs. If you are feeling brave, you could try manually by going to ~/.idea/libraries and edit play_services_x_y_z.xml (x, y and z are the version numbers you are using.) Look for the <JAVADOC /> tag. Modify it to be <JAVADOC> and add a sub tag <root url="put_your_external_url_here" /> then close the javadoc tag.

You should be able to create a custom gradle task to inject the appropriate XML if the file ever changes so it prevents issues on gradle sync. But, it would be some work. It's really a function of how IntelliJ handles maven dependencies from within Gradle and the setup of its projects rather than it being gradle's fault, so I don't think there's any special gradle setting to make it work.