I guess if you're not planning on supporting curves or any sort of user-defined paths, then you can go ahead and store vertices for simplexes. But for any sort of curves and paths, you can't.
I think this really is the heart of the question. Can you? I suppose not, at least not with-out special casing GJK, or representing them as a high-res polygon. Which in my mind kind of eliminates the beauty of GJK to begin with right, as long as the shape has a support function, you can plug it in GJK.