I goofed in my answer to the original question. I said, "No" when I evidently meant to say "Yes". for I went on to argue for the "Yes" answer. I was evidently sleeping peacefully when I wrote that "No". To the extent that matter occupies spacetime, it follows the curvature of spacetime. I used the image of our Universe as laid out on the three-dimensional "surface" of a four-dimensional hypersphere. Objects on thaat "surface" follow its curvature. That curvature might be nearly negligible for a small object like a planet, but it becomes very significant for an entire galaxy.