Depends on the country, and I'm not sure it's the same effect, ie not being able to pass culturally due to upbringing mismatch. Probably true for those growing up in very poor, crime ridden places where they can't learn the basic hygiene, punctuality etc needed for work.
As for social mobility, anecdotally, from who went where in my circles, tech and engineering are definitely higher in this than law and economics. Whatever is more concrete and harder to muddle the waters, is better suited for outsiders as a ladder. But the really big money is always in softer things but they a better gate-kept. I don't really think anyone tries to gatekeep the hard fields or trades too much. It's also why "the Polish plumber" is a meme. Easter European immigrants can take up such jobs and often reach a middle class income. I know many simple hardworking people who couldn't progress much due to cultural fit, but do make decent money in England/Germany etc. with physical work (like transporting stuff, setting up stages, cutting trees). Their kids do have a chance to enter the cultural middle class then.
It would be interesting and possibly revealing to research the source class of tech workers to see how many don't come from a middle class background.
The only research I could find at short notice was this from the UK:
https://www.bcs.org/media/1652/social-mobility-report.pdf
The UK and the US both have poorer social mobility than Europe, so the figures in the US are likely to be even lower than here.