Interesting. As it turns out almost everywhere I "Overland" signal is poor/non-existent so I tend to have my phone off or in airplane mode anyway. However, sometimes I bring a small Bluetooth speaker and play music I previously downloaded, so I'd leave a BT signature. That said, Class 1 Bluetooth has a 100 meters range... if a threat is already within 100 meters of me I suspect they're already aware of my existence. I think most phones are Class 2 and cap-out at about 10 meters.
-TJ