unless the FM radio in question has Bluetooth connectivity to connect to external speakers the the answer is no. You would need some sort of adapter that would most likely connect to the AUX port on the FM radio to transmit the audio wirelessly to the Bluetooth speaker.
You can connect a bluetooth transmitter to the audio output of any tuner. FM tuners don't have AUX inputs but if you wanted to use a receiver you would connect the transmitter to a tape record output if it had one.
Personally I would just use an Amazon Echo Dot rather than a tuner. Tunein and IHeart radio will give you all your local channels plus a world of additional choices plus add voice control.