You can't create in software what isn't there.
You can add artifacts but that's about it and it will actually distort your signal.
I'm not too sure why anyone would worry much about "distorting" an already horridly distorted signal.
As noted in my original comment, software processing will not unmix an already scrambled egg. However, I have seen situations where the reprocessed song is a more listenable improvement over the original.
Does it even remotely approach what I would have wanted had I been in the mixing studio at the beginning? No. Can it be a bit more listenable? Yes. Below is a track from a Morningwood album. The left (top) channel is in its original state. The bottom channel, which was very similar, was reprocessed to reduce the amount of clipping. It didn't add sounds (artifacts) that were not present before, it just readjusted the dynamic range based on the software's algorithm. Guess which one sounds a bit better? Not perfect, just a bit better.