Of course they do, or they would not be very useful given the number of horribly-built websites today, but even the JS-enabled screen readers can get confused b

Of course they do, or they would not be very useful given the number of horribly-built websites today, but even the JS-enabled screen readers can get confused by dynamically loaded content, sometimes getting it in the wrong order or not being able to access content that's triggered by things like infinite scrolling. Still, requiring JS for core non-interactive functionality is a net negative for any website. Why spend more effort on making your site more annoying?