No. When my phone is not in use and the screen is black it occasionally shows the time with a lock (power saving thing with Droid Turbo 2) When I have any other notifications from other apps such as FB messenger or missed calls, an icon for that app shows up under the time in the black screen to...
Notifications off/on, pop up window when not in app (tried this one and that's not it), vibrate, ringtone, wake screen off/on, LED color, privacy-- show "new messages" instead of content.
I've tried all of these 🙁