I'm not sure I understand the question.
>first template image
Does this mean the first attached image with the pants, shirt, etc?
If so, no. That is a texture image for the clothing 3D model/s worn by the default players, other models (like the player's skin, or custom models) need different UV mappings. The kit's UV map (defined by the kit's 3D model) was specifically made to unwrap all the faces of the kit model onto a convenient square image.
Each model contains its own UV mapping, which we can modify in Blender. I could make a player that is just a cube, which only has six faces, and use pic related as the shape of the UV map.
The only reason the current Lego man's UV map is bad is that it didn't come with a pre-made one and I don't know how to properly
unwrap most shapes yet.