Immigrants cannot be lumped into one homogeneous group. They range from highly educated "upper society" members to nearly illiterate poor refugees. So it depends on who exactly you're talking about.
Some immigrants are highly educated, have high incomes, and a lot of wealth. The richest cities and counties in Virginia, for example, have large and diverse immigrant populations. If you think white = rich, you need to rethink that. Asian-Americans, notably Indians and Chinese, have higher household incomes than whites.