That's not really accurate, as screen readers read the page that's present in the modern browser (IE, Chrome, Firefox), including whatever has been done with JS

That's not really accurate, as screen readers read the page that's present in the modern browser (IE, Chrome, Firefox), including whatever has been done with JS (mostly), so even if the initial page is fine, your progressive enhancements may yet make things inaccessible. A very common problem is assuming mouse-only input for buttons or menus, making them not work from the keyboard use.