That option can be disabled by turning off "Find My network" such that the phone will be off and radio silent. With it on, it will continue to beacon until the battery reaches the final BMS low voltage point.
It doesn’t, as far as I know (or rather, it might turn off the ability to ping the phone, but passive Bluetooth/Find my cloud location should still work).
And even if it does, turning on Airplane mode is not possible anymore for a locked phone.