Electret Microphone recognize music with FFT
For sure.  

The electret will pick up sound just like any other microphone.  There are a few draw backs though.  You will be limited by the range of frequencies you can pick up with this type of microphone.  I'm not sure what range you can expect but such information would be listed in the microphones datasheet.

Once you are able to get the analog stream from the microphone, you can analyze it using a suitable FFT algorithm, such as FFTW.  It is from those, you'll be able to extract various peak frequencies within the music.