Yeah I've tried this, I desperately wanted to a'capella the track "A Winter's Tale" once.
The effect works. I took my voice (just reading lines for a narration I did) and double-tracked it with a different line of speech. Then I tried this acapella method and it worked, it completely eliminated the 2nd line of speech.
The problem is, your two waveforms have to be *exactly* the same with regards to the thing you're eliminating, it seems. It's not enough for them to sound the same, or even be the same recording - the volume and shit has to match as well.
It might be very possible to get stuff like this to work if we completely avoid using mp3s, and merely stick to CD-rips that are not compressed at all. Even then, different mixing in a karaoke version would play hell with the idea...
for the record, my acapella of A Winter's Tale never worked. It just got rid of some of John Deacon's bass. :(