When lowering my game resolution I reduce the pixel count of the final rendered output image, does the 3d model I use to render the final image also lose polygons?
No your meshes do not lose polygons. Only the amount of fragments generated by the polygons will be reduced. If you think about it, where would the polygons go? You still need all of them to make sure you have correct result when rendering your scene. Even the sub-pixel sized polygons are usually included in final image.
In some cases though, the rendering can be optimized a bit to find and discard polygons that are way too small to be affecting the rendering result. But in these cases the mesh data should be pre-processed before rendering.