Would things like past class distinctions show up in data like this?

Like say everyone tended to marry withing their own class at different points in history, they might tend to be more related to other people with ancestors in similar classes, than in societies that abandoned it.

Not endorsing it but would be interesting if past social systems affected DNA.

That's extremely likely. Indeed, for (a) ethnicity and (b) geography, it's obvious that these correlate with ancestry; people tend to marry within their neighbourhood and within their clan. That's one reason why the principal components of genetic data tend to map rather neatly to geography, and why genes can be used to make inferences about past populations.