Topic title and description are pretty much the question.

I'm starting up a new unarmed oriented character soon, but for an extra challenge I'm thinking about having them use no "unarmed weapons" at all (no brass/spiked knuckles or any fist weapons). If I take the Piercing Strike and Paralyzing Palm perks, and all the other associated unarmed combat perks (like Slayer), will this be a viable character build able to take on anything (like Deathclaws) or am I severely gimping myself to the point of unplayability?

Unfortunately your fists have little in the way of DAM hence the second you try smacking an enemy with some decent DT you will find yourself completely unable to damage them (or do something like 1 damage per hit which also is nothing).
I don't think its possible to kill a deathclaw with your fists. Then again someone probably has by using paralyzing palm and non stop knocking it down but that would only work 1v1.

IIRC Super Slam works on barefist. I would say if you choose your opponent wisely you can beat the game.

I would'nt try it, it does'nt go well. I suppose boxing tape is close enough to bare handed to count. Boxing tape does decent damage.

I have a female unarmed fighter called Panjor'il.
I can hit hard without weapons but not nearly as well as with weapons. But I would'nt fight anything that was not really low without weapons. Definately not a deathclaw, shudder. I can't fight White Glove Society people barehanded. And thats on very easy. You would'nt be able to do it. You'd have to use boxing tape at least. Or knuckledusters.

If you put all you you can into unarmed perks, you can hit very hard. Put a load into strength and endurance.

I think you would make it VERY hard for yourself if you only fought barehanded.
You probabely could'nt do it. I would'nt fight barehanded when there were weapons, for sure.