It shouldn't matter what the original song genre(s) were, just as long as it was done in a metal music style for the cover.
One of my all-time-favorite metal covers is of The Postal Service - Such Great Heights, which was covered by Confide. (Note: The Metal starts around 40 seconds in.) It's blend of Metalcore and Screamo made this cover of this song made it stand out once again for me.