Yes, his violence would be right at home in MK, but his speed wouldn't.
In MK doom marine would probably be just a guy with an obnoxious projectile that other characters will struggle to deal with due to their stiffness and cool fatalities. but that is not actually doom.
Say what you want about ripping demons in half, thats not what makes doom fun or doom. thats an addon that makes what makes doom fun more satisfying. And that is rushing trough enemies, stayuing mobile to survuve while closing to maximize your damage on that ****ers. and if this doesn't translate well into smash bros?... i dunno what would.
Plus he certailny can have a couple of crazy projectiles (wouldnt be teh first) and a cool grab game, and i think we are golden. I think that if his grab are as visceral as say, Bayonetta's Final smash, or Ridleys side B or Down B, we will be fine.