MP3 is compressed, so the two extracted 160kbps mp3s can't just be added together to exactly recreate the original. WAV is easier for this question, separating every other sample into its own file and halving the sample rate of each.
I would think that this would be the same as splitting an image of copyrighted text, such that every other pixel goes into another file (filling with white or a copy of the adjacent pixel).
In the image case, it would be easy to put one of the copies through various filters and OCR the result, producing the original text in its entirety. I'm pretty sure this is illegal since the text is the material under copyright, not the representation of the text. The same could be said about sound media. The record of the performance is copyrighted, and any work produced from that performance is protected (subject to fair use).
There are a lot of people on here smarter than I am, so please debunk or clarify where needed.