Would it be possible/feasible to play a character that goes unarmored or would that only serve to hinder/kill said character?
It depends. There are some talents that give you bonuses when you are unarmored, like the Martial Arts tree. Also, being bare-chested means you have more room to display war paint. Pictish war paint for example grants you 5 Courage Soak.
So yes, I think it is feasible. It might not be as strong as wearing armor, but will look really cool.
In most original stories by REH Conan wore armor, and as good a suit of armor as he could get his hands on.
In the Conan 2d20 RPG there is quite a downward spiral after a character gets the first wound.
Armor allows you to sacrifice partial armor to avoid taking a wound. That is a very important feature of armor in Conan 2d20 (see the above mentioned downward spiral).
The Conan 2d20 RPG supports less the very cliche “naked barbarian” trope propagated by the epigones of REH. It is in this regard rather true to the source. Wearing armor is in most cases a very good idea. Not wearing armor is often a shortcut to your grave.
Sacrificing armor piece is critical for the survival