Depends. Since Apple/Google are monitoring it on their end, and I believe (at least on Android) turning off notifications at the OS level just blocks it from sh

Depends. Since Apple/Google are monitoring it on their end, and I believe (at least on Android) turning off notifications at the OS level just blocks it from showing on your phone, these would still be sniffable. If the application in question has the ability to disable notifications inside the application itself, that should work.