would that work as a pink noise signal to play while calibrating?

Negative. That is an MP3 file. Don't ever used lossy-data-compressed audio files for calibration, use WAV files only.

Most audio editing packages will generate test audio tones for you, and most of the calibration spectrum analyzers will also generate test audio tones. These can be save to a WAV file and put onto the player for playback. Watch that volume control when you're doing it, as the volume level of these test tones will be considerably higher than regular music. You could damage your speakers and/or your ears if you're not careful.

I prefer using frequency sweeps and combined frequency bursts to pink noise anyway.