Import the Audio comp library. You can do:
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add (\:red_circle\: record :: sensing) to (my [sounds v] :: sensing)
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Run that, click the record button in the pop-up, then play the music.
So the basic answer is "sure why not?" with the caveat that your recording will likely include a low-fidelity copy of the instrumental by way of the computer's speakers and microphone.
Just did a quick trial and this method definitely works. Possibly could separate the instrumental from the vocal through use of headsets. Will explore further tomorrow ... thanks for suggesting this method!
A variant of this recording method might be to display a metronome on the stage to control timing / pacing while recording; then play back the vocal track in parallel with the instrumental.