I'm assuming you meant unarmed.
Will it be viable? Sure. Pretty much everything will be viable. You can just turn the difficulty down in the worst case, but I'm sure some challenge runners will do hardest difficulty unarmed runs.
Will it be competitive to armed? Almost certainly not. It just can't match the number of uses a ranged weapon can have. Using ranged you can have a sniper, assault rifle, and shotgun. That'd cover every distance. Unarmed you have to close distance before you can even start dealing damage, and once you do presumably you'll be out of cover and others can shoot you. It's a single player game though, so who cares?