Yes, it's possible. You will need to install Sound Flower and create a new aggregated input device (soundflower + your mic) in AudioMidiSetup.app (comes with OS X).
Then choose soundflower as your audio player's output device, the aggregated device as the mumble client's input device and you should be able to stream in
the music. If you can't hear anything through your headphones/speakers you'll need either to run SoundflowerBed.app or create a multi output device.
Just google around on how to do this in detail as it's a little complex and I don't have time to explain it now
(Oh, but first check if your mumble client doesn't have the option to play back audio files into the chat!)