My answer, much like Krom's, is that it depends.
In cases where you have large swaths of polygons being obstructed by another object, it's likely going to be a good idea to cull objects that are completely obscured. Suppose you are looking at a wall made of two triangles, and behind it are several objects composed of several thousand polygons. If you draw everything, you waste valuable GPU time. But by culling the objects behind the wall you can turn a draw call of thousands of polygons into a draw call of only two polygons. In this theoretical scenario, you likely would not see a massive difference in performance as a few thousand polygons is nothing to a GPU. However, when applied to larger scenes the performance gains can be quite significant.
On the inverse, and as is probably closer to your scenario, when dealing with a minute amount of polygons being obscured, while it may technically be slightly faster to draw a different model that has the obscured polygons removed, the gains will be minute, and almost definitely invisible. In addition, you will have to factor in the memory increase by loading in the alternate model. (Or models, assuming you have a different one for each area that can be obscured on your character)
Specifically, in your case, it's unlikely that culling the few polygons will do much for you, but it's always wise to do an A-B test to determine if that's true.