No, not really. That doesn't mean that they don't, anyway, it's just that it doesn't follow from the premise.

This depends on how you structure the argument. It is a strong response to "races cannot vary in brains" to say "what generates that fact that would not also generate the fact that races cannot vary in skin, muscle/bone structure, genetics, and maybe other things?", because this is pointing out that the claim that races have identical brains needs complicating features, or else it gets other questions obviously wrong.

We do not know much about individual variability of the genome, and as such we do not know much about what parts of the DNA are affected by individual (a posteriori, ethnic) differences.

What do you mean by 'individual variability of the genome"? You know that we can actually sequence human genomes, right? And that this has been done for people of many different racial groups, and we've identified the areas that people vary, so that you can get your SNPs sequenced and your racial ancestry estimated cheaply?

A recent experiment, for example, showed that there is more DNA variability within a single ethnic group (subsaharians, probably the most ancient alive today) than within different other ethnic groups.

This is entirely unrelated to the question at hand, and you seem deeply mistaken about its relevance. (If this is true, and it is, doesn't this mean it's obvious that we can tell apart the ethnicities by looking at their DNA?)