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Someone has done an empirical inquiry into this question:

1) This site shows that mp3 encoding does not affect binaural beat quality, even if its encoded in joint stereo:

http://www.geocities.com/thiwankaw/articles/binaural_beats_and_mp3.html

2) A more recent article by the same author argues that joint stereo does affect binaural beat quality (which contradicts the article above):

http://www.geocities.com/thiwankaw/articles/joint_stereo.html

I've e-mailed the author to see if he has an opinion on this discrepancy, but the e-mail address doesn't work.

I think the moral of the story is that if you're going to encode your own binaural beats, encode it in normal stereo, just to be safe. If you've downloaded a joint stereo binaural beat mp3, I would analyze it myself using CoolEdit or GoldenWave, etc. to make sure the frequencies are correct.

Are there any technically-inclined members of the community that want to do a couple of tests with joint stereo binaural beat mp3s to settle this question once and for all? I can provide some test mp3s if anyone needs them. extra1z{at}yahoo<dot>com...