Most likely that would have happened, at least if there was a major depression as actually occurred.
I was just thinking that the black civil rights movement might well have been handicapped from not closing immigration, since the Eastern European immigrants were even more racist that the French or the English tended to be. Moreover, it is an unpalatable but true fact that black civil rights has progressed best when immigration has been lowest. This was true not only during the 1950#, but also in the early 1800s when
Mark Thornton showed a quarter of a century ago that the free black population grew by 180 percent during a period of extremely low immigration (which Thornton fails to note as such), yet ceased during a period of immigration increasing.