I think it depends on the accent. There are plenty of high status/upper class people with national (Scottish, Welsh, Irish) or London/West Country accents -- even pretty thick ones. On the other hand, a heavy Northern/Midlands accent is pretty indicative of a lower class background.
"For example, the first "fully human" AI will easily win the chess tournaments, simply because current AIs can already win them."No they can't. *Chess playing programs* can easily win tournaments, self-driving cars and sentiment analysers can't. An AGI that had the ability to run a chess playing program would be able to win, but the same applies to humans with the same ability.