Sadly, no. The nanobots will be used for very bad things. To give you an idea, imagine a nanobot that will go into your cells, detect your race based on your DNA, and then decide to kill you or not; imagine how bad dictators can use these selectively against whole groups of people. It's biological warfare on a completely new level.
"In conclusion, neither mtDNA nor Y DNA can give any hint as to your “racial” membership in U.S. society. Autosomal DNA, if very lopsided to one continent or another, can suggest what you look like. But this does not work for those Americans who choose to self-identify as Black despite having mostly European DNA, nor for White Americans unaware of their African DNA, nor for Hispanics, whose “racial” membership is determined by their culture, not by their genes".
I guess the evil dictator the parent describes can skip this category: ("this does not work for those Americans who choose to self-identify as Black despite having mostly European DNA") and spare: ("white Americans unaware of their African DNA"). In fact, that evil white dictator would probably want to do so, even if it wasn't a technical limitation.