Well, they were important early on. We wouldn't have built the Marine Corps as quickly if we hadn't had to deal with Muslim piracy in our first foreign war ("...to the shores of Tripoli"). And, one can justify a 500 year time-frame: Columbus would never have sailed west if it weren't for Muslims making trade between Europe and the Far East via the Indian Ocean and along the old Silk Road impossible. (I know, he might have had a Viking map and expected to find "new" lands, but the funding was justified on the basis of finding another, non-Muslim-infested route to the Indies.)
Somehow I don't think that's the take the course will offer, but there is a legitimate case in actually factual history for noticing the influence of Islam on America's history. Yeah, they've always been part of "the American experience", but it's always been rather like the way they were part of the "American experience" on 9/11/2001.