I just checked, and by default, JAWS reads <hr /> as "dash dash dash dash". Presumably some JAWS users customize that, but my configuration is out-of-the-box, so by default the horizontal rule is accessible to screen readers.

And this, actually, is an extension of what people have been saying about semantic markup. Using the horizontal rule tag means that you can trust the screen reader to do what is necessary (configurable by the screen reader user). That means that if you've been using it, you are already being much more helpful to people who use screen readers than people who customize their own section break with something like "~~~~".

By the way, it's awesome that you are thinking about this so much!