I am a firm believer that there are many privacy techniques you should focus on before encrypted messaging because they will offer you much more “bang for your buck,” things like good passwords, two-factor authentication, and even encrypted email. That said, I still believe that encrypted messaging is a critical part of a well-rounded privacy and security strategy. While the vast majority of our day-to-day conversations may be benign, it can still offer a lot of insight into who we are as people – our routines, likes, and personal thoughts. This information – mundane or not – is worth protecting.
If I remember correctly, it depends on the notification strategy. If your service is throwing the entire message into the Google Play Services, that’s gonna get logged.
But you can just send a “wake up” message the your app, which then contacts the server privately to see what’s up. I believe this is what Signal does.
There’s no perfect solution, if every app installed their own notification service your battery would die. There are custom play services out there but let’s face, the vast vast majority of users never even heard of them.