You mentioned at least one significant area where they were worse workers, and where their ability to advance would be hindered by their inability to write their thoughts in effective English. Higher level jobs involve significantly more communication, so while you could get by without being able to read and write well, it isn’t exactly a good thing.
I have met too many engineers and engineering students, most born in the US, whose writing skills are beyond horrid. Their level of writing is certainly worse than that of any competent high school student. So good writing skills are not a given because you were born in the US. And besides the obvious hindrance of communication, the act of following good style practices in code is important to being productive as a software engineer, and very closely related to the ability to follow the mechanical rules of language.
And I have seen a number of studies that show that better grammar makes one a better programmer.