If you can see your emails on your Android device and Google is admin on your device, why do you say that it is impossible for them to read your emails? I don't mean that they could read them in the cloud but if they can read them locally on your Android device and for example they could send a message back to Google saying "I think this guy should get ads for a new router".... but of course they could do much worst (they could send whole messages back for example).
Android was designed to leak as much information about the user as possible all the time, even to third parties. Spy satellites have less invasive software.
