We don’t know because this is not the question we should ask. Design and code represent the same thing and therefore must be connected. It doesn’t mean though that they require the same person to take responsibility of both, just as the songwriter and the singer can be two different people creating one masterpiece.
The foundation and core values of Agile are highly important, but we shouldn’t be slaves of our processes. We’ve learned how cycles, iterations, quality and time are the key ingredients of a successful product. What we can cook using these ingredients is the interesting part.