Some peasant children who achieved prominence in society are more deeply and genuinely aristocratic in their ways than offsprings of the hereditary noble. Yet it seems an exception, not the rule. Even among peasants who never achieved anything you can find people whose bodily constitution, posture, manner of speech, etc. make them more suitable for high-society parlors than 90% of their frequenters. Do Russians pay attention to that natural-born nobility? Definitely so.
Reading Sad Cypress by Agatha Christie (my wife’s vacation paperback; Russian translation sloppy), I was surprised at the words of an English nurse (who turned out to be the root of all evil in the end but whose judgement was accepted by Hercules Poirot as something to be expected from a regular Briton) insisting that it was much better for a certain young girl to keep thinking she was the daughter of humble but honest parents than — oh what shame! — to learn that, in fact, she was an illegitimate child of two wealthy gentlefolks. And that between the Wars! On the contrary, an illegitimate child of a noble in Russia would be considered to rank well above his nominal parents — typically peasants. (I mean the 18th century and the pre-1861 epoch.) Zhukovsky, Hertzen, Fet (Foet?)-Shenshin were illegitimate sons of their fathers. The first count Bobrinsky was the son of Catherine the Great and Alexei Orlov; the baby was carried away from the empress wrapped in his father’s beaver fur coat (beaver is “bobr” in Russian). Or take Dostoevsky’s The Adolescent.
Apparently, “noble blood” made a difference for ages; it’s surprising how it stopped making a difference after 1861 (suddenly it mattered again in 1917, in a perverse way, but this all passed by the end of the Great War); most Russians are probably descendants of pre-1861 serfs now.