So you are saying that ~250K immigrants that have been living in the US for up to 6 years (work visas last up to 6 years) are now going to stop renting and buy a house next week. It sounds that rents will go down around here.
Most immigrants like the engineers that work at Qualcomm have not waited for their green cards to buy a house. They do not need one to get a loan and, as long as they are employed, obtaining a green card is quite easy. There is little risk in buying a soon as you get off the plane.
BTW Every year the “backlog” is released at some point, just like this year.