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Yes
Forget frame dragging or the movement of our Sun in the Solar system, or the bary centre of our solar system, or our solar systems movement around galactic centre or that centre moving with respect to the local group or the Virgo super cluster etc.
If you like imagine the Sun and Earth are fixed in space, there was no such thing as gravity and accept the Earth is rotating. Realise it takes light takes 8 minutes to reach the Earth. The observed position of the Sun will always be off by the transmission delay versus the rotational speed of the Earth. If a solar day was 32 minutes long in this scenario the Sun's observed position must always be 90 degrees away from its true position.
Bojan - a space based LIGO system should be able to detect and anomoaly between GR and the observed position of the Sun. If the Gravity field of the Sun is not centred at the observed location of the Sun, then you have a delta between the speed of light and how a gravitational field radiates.
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