It was not totally unknown for trips back to the old country by those born in the US, sometimes for a visit other times mothers would become homesick and take children back home with the idea of staying. But with 2 world wars this did not work out.
Let me know if you would like any help finding them on ship manifests. I have searched for hundreds of people and have been sucessful in finding those who are hard to find. Oh just in case you are not aware Ellis Island, which was the immigrant processing station for the Port of NY, was not the only port of entry. Others were Boston, Baltimore, Philadelphia (where I have seen many from Russia), as well as the Canadian Ports of Halifax and Montreal.