Yes, a high school class focusing on the U.S. Constitution would be useful, because it is the most important document to this country. Any discussion of the Constitution would have to be part of a larger discussion of philosophy, the Enlightenment, natural rights, and whether there is such a thing as absolute good. It would be an interesting class.
I believe that as Americans many are uninformed on what the U.S. Constitution holds. I know in my high school, I learned about it briefly in freshman year and slightly more extensively in junior year with American History. However, I feel a senior year course requiring the full and intensive study of the document would be very useful. All Americans SHOULD know the law of their land! I'm not saying this will automatically make Americans more informed....But it increases the chances. The course I imagine would discuss the writing of the document and the meaning and it would detail the Bill of Rights and all the other amendments. Students would analyze real-life cases where the Constitution was violated and upheld and learn intensively about the Constitutionality of the law. Students would practice it in real-time with a mock case and write their "Supreme Court" ruling based on what they've learned.
I say senior year because by then you should be ready for college or to move on. The course could have a regular and an honors version. The Honors, of course, being more intensive. The regular probably would still be hard and complex but I still feel it'd be necessary that all high school grads at least get a grade of a C in a course understanding the Constitution.