Yes, this is a huge effect relative to the stability and accuracy of modern atomic clocks. Even a few hundred meters of elevation difference on earth is easily visible in clock comparisons and has to be accounted for.
Re:NASA is working on new clock for the Moon
by robertlagrant on Saturday April 06, 2024 @10:14AM
(#39952586)
But to what extent? 1s a day? 1s a century?
However: Is this difference of a magnitude exceeding everyday nonrelativistic clock drift?