In my experience, there is definitely a correlation at the least. In today's world, unfortunately there are a lot of options available for people with great communication (written and verbal) skills and employers can choose. I am not talking about Accents but if you cannot formulate a coherent, grammatically correct sentence, you will probably do lousy work. I have seen it enough at least in my case to make that assumption. Also, not everyone needs to be a native English Speaker (I am not one myself). So this is not a racist thing either. It is simple facts of life.

Even for hardocre programming roles, you need to be able to ask questions no matter how junior you are.

When I see a Resume with obvious typos and grammar issues, I usually skip unless it seemed like a genuine one off mistake and I have spoken to that candidate already.