Will it? Vulkan is meant as a low-level version of OpenGL for vendors who want to optimise their engines and have more control over draw calls and whatnot. Does it actually add any features that will be noticeable in a small, static scene?
So, in practice, if they are noticeably different in the dynamic case, you'll see those differences in the "as if it were dynamic" case, which is most graphics demos of this sort.