Because the surface of the Earth is continually accelerating, as you pointed out, noon and midnite approximate two different inertial frames, but in each one, if you measure the round-trip speed of light, you will get the same value.
Prior to this fact becoming known, this is essentially what the famous Michelson-Morley experiment (MMX) was trying to take advantage of, assuming that the speed difference relative to the sun (or the stars or whatever) would be detectable. But note that the speed difference you are talking about has a direction to it, the North-South component of the speed would be the same at noon and at midnite whereas the East-West component would be different. It would have been extremely difficult to make a precise enough measurement of the East-West component of the speed of light at noon and compare that to the same measurement at midnite, twelve hours later. So instead of doing that, they compared the East-West measurement with the North-South measurement, looking only for a difference in the two. But they could never detect any difference, no matter when they did the measurement, at anytime during the day or night nor at anytime during the year. The North-South component always matched the East-West component, as well as all other directions in between.
So this was the first experimental evidence that the answer to your question is "no".