When my phone is connected to my car stereo via BT and I get a phone call the car speakers "ring". No matter what source I'm listening to on the stereo. This is normal and expected.
I would like other notification sounds to act the same way. Facebook, SMS, Gmail, etc. I want the car speakers to transmit this sound. Even when listening to the radio, or XM. They will do it if listening to BT audio, but not without.
It's probably not possible, but I've been known to be surprised before. I've checked XDA, Xposed, Play Store, and Google.