Hard to do it without being a vesk, I think.
My vesk soldier is doing fine and my stat array isn't necessarily conducive to unarmed. I've got improved unarmed for the dice scaling and at level 6 I'm doing as much with unarmed as I would with a light reaction cannon. Highly dex-based character (started on the premise of ranged), so my unarmed suffers slightly in that regard.
The vesk special (1.5x level to damage) is really important to the success of unarmed. I wouldn't recommend unarmed on other races.