From Mr. Tuppence:
Not at all. What is being measured with the earth's spin rate is one things. But what we are actually basing our whole time frame on is the time it takes the earth to go around the sun once in its orbit. This is a different quantity and is independent of the spin rate of the earth. Therefore, if the earth's orbital period is constant and the definition of the second has not changed (it is based on the earth's ORBITAL period), then the observed, measured changes in the speed of light are genuine and not an artifact of the earth's spin on its axis.