Using Doppler velocimetry with digital signals such as Bluetooth
If your question is whether you could ever use the Bluetooth radio in an iPhone to perform doppler velocimetry, I'm going to go out on a limb here and say no.

Most mobile devices are incredibly  modular. This means that the BT/WiFi radio (they are often combined into a single chip these days) is designed to handle all of the RF signal processing necessary, and then hand over only the digital data received, but never the analog signals.  By the time the signal is turned into digital data, any effects of multipath, channel noise, doppler shift, and other analog phenomena has been removed.  It is highly unlikely that any mass-produced cell phone would have access to the analog signal being received by the individual radios.