Like the answer for the descendants of Charlemagne, the answer is technically a yes, after countless generations of intermarriages, the genetic heritage will spread to a given size of the population. It is possible that even today there are those who still bear the heritage of the royal house, though they would likely not be of any significance . Even the Aisin Gioros are now little more than salarymen. It would be impossible to trace a specific lineage that far back with complete certainty. No record has lasted that long. So no, there is not some secret elite family like with the ex-royalty of Europe that we could confidently consider to be the continued direct familial legacy of the Shang.

One interesting point is that the traditional Chinese accounts actually had the succeeding Zhou dynasty appoint the Shang as dukes of a small fief rather than outright purge them, so this lineage supposedly survived long enough to produce some of the dynasties of the various kingdoms that emerged during the Zhou's collapse.