Can a COTS FM Radio transmit?
If you shine a torch on an incandescent lamp will voltage come out - no it won't. If you heat up a resistor will DC voltage come out - no but you'll get more noise voltage (a few micro volts maybe).

The back stage of a receiver is an audio power amp and you might see a few microvolts of signal at its input when you shout loudly into the speaker but, the big killer is that an FM radio uses a demodulator to extract the audio from the carrier and, when you force a signal on to the output of the demodulator, a fully modulated FM signal does not appear at its inputs.

To produce an FM signal you need a modulator and no matter how hard you might shout into the speaker, a demodulator run backwards does not make a modulator.

Next is the problem of the intermediate frequency stages. Next is the mixer stage and finally a sensitive front-end amplifier.

No it just won't work at all.