Um, yes. The United States of America was founded by immigrants, starting with the pilgrims on the Mayflower and continuing to this day.
White privilege is referring to stuff you don't have to deal with like having to worry about viligantes running you down and killing you because they think you're a thief or having some woman accuse you of sexual assault because you brushed up against her in a store or having someone pretend to call the cops on you because you are running a lemonade stand without a licence. When have you heard of a white person having that done to them?