The answer would depend on the nature of the course.
If your class is only about books that are written by Americans, or that directly address the American system of government, the answer is no, you should not read that book. Locke was British, and wrote his classic work roughly a century before the United States was founded as a nation.
However, if you are analyzing ideas that influenced the American system of government, yes, you should absolutely read Locke's book. Locke had a powerful influence on the leaders of the American Revolution.
Colonial leaders who were arguing against the Stamp Act called on Locke's authority, and people who argued against slavery or in favor of women's rights were strongly influenced by Locke.
Thomas Jefferson identified John Locke as one of the greatest men who ever lived, and you can hear echoes in "The Declaration of Independence," especially in the discussion of rights.