As long as the remix retains the original feel of the actual song, then I don't see why not.
For example, Boss battle music is really epic and powerful, so I usually expect to see something Metal or upbeat, whereas a song like In A Snow Bound Land (that IS the ice level music, right?) is very soothing, so I expect a piano or jazz rendition. But I'm not restricting these by genre. If the genre can still retain that original feel from the song while still being able to differentiate from the source in an original and well-composed manner, sure. I wouldn't see a Rap song of Crocodile Cacophony being able to keep the original feel, but we have some excellent talent here at OCR, so I'm not going to say it's impossible; surely it can be done!
Plus, Exor, some people here are willing to take creative risks and push those musical limits, so you can at least appreciate that aspect of Mining Melancholy being a Rap remix.