Dragon Warrior uses the noise channel from some sound effects - enter/exiting a town and climbing stairs come to mind (might be the same sound effect for both). I have yet to emulate the noise channel on the PCE version of DW, so you can hear the missing effect or solid tone in its place.
That's what I was thinking on the way to the pharmacy the other night... There *are* percussion-like sound effects within the game. The stairs/exiting town sound mentioned by Tomaitheous, which could be considered a low-pitched kick drum; the sound made when you strike an enemy (pseudo-snare); the "Excellent Move!" sound effect, which sounds like three hihat hits; etc.
Since the game already contains percussion sounds, that's half the battle won right there. I reason it's now just a matter of retooling the music engine to recognize and apply such sounds to the in-game music (and, of course, putting said parts into the individual song programs).
Somehow, I doubt this will be as easy as making SMB1 play percussion in the Underground and Dungeon levels...