I'm pretty sure that fortnight used to be more commonly used in the US, but it has fallen out of use in the past century or so. So to an American, probably the best comparison is the word "score" to mean "20." That was also in common use, particularly to describe years or age, a century ago. But except for the famous Gettysburg Address that begins "Fourscore and seven years ago," most Americans would never have any reason to know what it means.
With fortnight, I do agree that anyone who has had even a moderately rigorous education in literature in high school will have encountered the word. Not everyone would know what it means, but it does come up in both British and American literature. If my education is an example of anything, I had a year of American-focused literature and a year of British-focused literature, with a smattering of both mixed in to the other two literature classes I took in high school, and the vast majority of the assigned books were written at least 100 years ago.
So I'd personally find it weird for someone to argue the word doesn't exist at all, but I would find it equally weird to hear it in normal conversation.