No, you can't copyright a voice. That's come up with "cover" bands. A cover band can sound like the original; they just can't claim to be the original. ("Compare to the ingredients in Elvis").
A cover band has to license the underlying composition, but not the recording they're covering. (This means ASCAP gets royalties, but the RIAA does not.) In the US, there's a compulsory license for compositions, and you can record and distribute any song by paying a relatively modest fee set by law.
This is just automating the cover band industry.
In ten years or less, this will be a common feature in DJ consoles, and we'll hear songs from musician A as if performed by musician B.
