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No.
My frame of reference for this kinda cute example is just considering a Sun / Earth system; as all else for the purposes of this discussion is padding (its a irrelevant relative motion as there is no absolute set of spacial co-ordinates according to relativity).
Look at the Sun and you see it as it was 8.5 minutes ago relative to Earth time. We feel its gravity and see its position as it was 8.5 minutes ago too because that's how both the force carriers radiate and the warping of spacetime radiate in any relativistically compliant part of spacetime.
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