In the couple of days since I have asked this question, a number of visually disabled users and people have been kind enough to reach out to me through private channels. I write here to summarize what I've been told.
MathJax has accessibility options (which can be experimented with through its right-click context menu) that can produce subtitles for mathematics, and in fact the actual reading of mathematics is "ok". It's not perfect --- it doesn't sound natural and sometimes is incomplete --- but it pretty good. Really, this is an indication of how extraordinary the MathJax team is.
Firstly, it is (broadly speaking) possible to read a page. It's relatively straightforward to read the question title, question text, and first answer text.
To understand why is to understand screen reader navigation. A very common way of navigating a page is to jump from header elements, like <h1>s and <h2>s, and to hope that subsequent text is organized in a reasonable way. It is also possible to navigate from link to link (useful on a search engine page, for instance), <p> tag to <p> tag, etc. The further away from classical semantic hierarchical structure, the worse the page will be in terms of basic screen reader readability.
The title is in an anchor-link in a <h1> tag, and so is an easy landing point. Further, it is the only <h1> tag on the page, so "natural" navigation will land on it immediately. That's good.
The next text after the title is the question, so one can roughly get to that. Then one can read the question.
Navigating to the answers is also quite straightforward, since the answer-count is in a <h2> tag (and it's the top h2 tag, so it's very quickly accessed). But distinguishing the end of one answer and the start of the next --- or jumping between answers --- is very painful and annoying.
That's actually pretty terrible.
Many aspects of the site are also essentially unknown. The people I talked to thought that accessing data like vote totals is often troublesome. (Incidentally, it's relatively straightforward to find the first upvote and downvote links, since they're early links after the <h2> answers header. But there is less incentive to vote if you don't read vote totals). Similarly, reputation count and the identities of specific users are less important and annoying.
The prototypical interaction seems to go about like this. One googles and happens to find out that some question may be asked/answered on stackexchange. One follows that link, read the title and question to see if relevant. Then one reads the first answer and hopes it's useful. It is not hard to read the following comments, and if they are there then one might read them.
I wish that I had asked how often one goes through the trouble of finding and checking the vote totals, but it only occurred to me that I hadn't dwelled on this while writing this brief description.
