Yup this is definitely happening. However, I’m not sure how effective it ultimately is. India is an incredibly inconvenient time zone for US based operations. And salaries are creeping up in Bangalore (the preferred city for this stuff).
If it were highly effective, it already would have replaced importing the workers, since it's cheaper to hire them over there. But I've seen multiple companies go big on offshoring and then scrap it after a few years and hire domestic again because it went poorly. There may be a new surge of interest in it if importing people gets harder, but I don't suppose it will go much better than it did before.