Is Nocturne viable as a bruiser?

None of his stats or abilities have any advantages, so no, not really. You could try it, but it would be very suboptimal.

I've seen a few Nocturne tops, and they usually go Titanic Hydra/Black Cleaver with Lethal Tempo. It's........okay? It doesn't really play to any of Nocturne's strengths, the biggest of which is being able to show up out of nowhere and pick someone off. A bruiser build won't let you do that unless the target is VERY squishy. Extended fights aren't really his thing unless you're going for an on-hit build.

He's certainly given me my share of bruises.

I'd say if the enemy doesn't build Grievous Wounds, he can be a bruiser.