yes actually it does!
It needs some work with focusable things, I needed to use the special navigation keys (I tested with ChromeVox on the desktop) to get to the lists on the left and right, and to click on anything i had to use the special "click" keybinding instead of pressing enter, but it's 100% usable.
On android it works great, about the same as any other website or app (i used the android accessibility screen reader to test)
Modern screen readers are just as capable as the rest of the browser, the only place they fall short is in image-heavy sites that don't have alt tags. Obviously you can greatly help by adding things like aria tags, and using markup as much as possible, but it's not like they just don't run javascript.