No method is provided of figuring out how large an object is that is referred to by a graphics handle.
You can get an approximation by using struct() on the handle and checking the size of the struct. However, graphics handles often refer to other graphics objects, and it is not uncommon for graphics objects to indirectly refer to themselves, so you would need some code to recursively descend the object without loops, adding up the sizes as you go.
Such a tool is generally possible; I have had reason to chase through graphics trees myself. But it is a fair bit of work to get right, and Mathworks keeps updating the graphic object representation, so you have to keep updating the code with every new release.