While in general, baring an unusually vindictive justice system, I would say no in an ordinary criminal sense. HOWEVER, the third imperium is feudal, with feuding houses from the Imperial family on down. Feudal house systems have a nasty historical precedent of "don't leave defeated house members(including children alive to continue a vendetta later". For example, the roman empire practiced "prosciption" the criminalization of being a member of a banned house, Augustus ,was well aware of how he came to power after the assasination of Julius Ceaser, and the plotters mistake in not killing off the julianni house. He probably had Cesareon(the child of julius and cleopatra) offed after the defeat of Marc Antony and Cleopatra. In any case Roman law allowed houses to be proscribed. Usually in most feudal societies,, the winning houses do the extermination of defeated houses extra legally, but sometimes it is dressed up legally where even being a surviving child is a capital crime of treason. with all the killing in the 3rd imperium during the civil wars(including the precedent legalized murder of emperors and family) i wouldnt be the least bit surprised to find out that proscription of "treasonous" houses is the legal norm. And if you are justifying murdering noble children, it isn't all that big a leap to justify killing commoner children in order to "remove" criminal bloodlines.
Also, the kkree two thousand worlds and the aslan hierate practice feudalism and feudal clan systems respectively. I wouldn't be surprised to have clan vendetta rules/laws to finish off opponent houses/clans. And with the Vargr, the correct answer to any question of do "they" do this is always "c" - All of the Above.
Even the zhodani,while using the tlaceverde to do mind altering of prole children to despise the actions of "criminal" parents, they might have a problem with noble children, who being psionic, are resisitant to the mind altering of the thought police. The consulate may well have decided that "problem" noble children, are an exception to the mind alter and let them go rule
Chumbly