Regular sound files will have an even amount of time spend energizing the coil positive and negative, so the motor will not spin around in the normal sense. With a strong enough amplifier it will produce the sounds in the file like a speaker, but it will not noticeably turn.
Actual PWM varies the percentage of the time the signal is HIGH in a fixed frequency square wave, thus all the different values are the same "pitch". Audio varies amplitude and frequency, but the cumulative effect of audio waves is neutral, it spends half of the time below neutral and half above neutral voltage. The simplest analogy I can think of is audio being itself, even vibrations in air, and motor PWM being wind.
I am not sure if it possible to generate a sound file that would turn the motor, it probably depends on the file type. In any case, you would be better off with a far simpler amplifier like a transistor, MOSFET, or H-Bridge on one of your nano's actual PWM pins.
As to whether or not you could analyse the file on arduino, it also depends on file type. The code for the arduino WAV sheild I've seen does not have the arduino actually processing data, but It should be possible with a simple enough file type for arduino to decompress. WAV is not normally compressed, just raw data, so your limits are the RAM and if you can code something to glean volume from the raw data. I don't have much experience in that kind of file processing on AVR so I'm not going to call it either way.