I think the more important question here is exactly what does seating depth due to affect precision? I've heard explanations that include tuning muzzle exit to the barrel harmonics, bullet alignment/entry into the lands, neck release, and a few others that I can't even recall at the moment. My point is that knowing exactly what seating depth does to tune group size should allow someone to better predict whether changing velocity should affect optimal seating depth definitively. Unfortunately, I am not convinced that any of the explanations I've heard over the years for what seating depth actually does to optimize precision are correct, or at least the whole story, so I don't have the answer. I've often wished I did.
In my hands, large changes in velocity do seem to require different seating depths for a given bullet on occasion. By "large", I mean velocity changes well outside the ES/SD for a given tuned load, such as when adjusting charge weight to hit the next higher or lower node, which might be as much as a 60-100 fps velocity change (or more). Much smaller velocity changes such as are typically observed when changing the charge weight by a few tenths of a grain (i.e. perhaps 10-20, or even 30 fps) do not seem require any change in seating depth.
At the end of the day, simply conducting a seating depth test when some other parameter of a load has been changed is simple and straightforward enough that it is possible for anyone to empirically determine where the optimal seating depth for a specific bullet/load should be. In contrast, the experiments and/or equipment necessary to rigorously define exactly how seating depth affects precision likely preclude many of us from going down that road when we can simply carry out a seating depth test to answer the question. Nonetheless, understanding the specific mechanism(s) by which seating depth can facilitate very significant and obvious changes in group size/shape would be useful, if only for answering questions such as the OP posed in a predictive manner.