Yes, it does. I think you have something weird with your browser: with JS on, it does a light AJAX request, without it, it does the whole redirect thing.
The request is the same. The buttons are <a> tags. Without JS, the link is clicked and does a full page reload. With JS, the click is caught and sent as a AJAX request where the response is ignored.
It's not any lighter, it's just not reloading the page.
Whoops, you're right, it does work either way. The response is the same with or without JS though, it just doesn't do anything with it when JS is enabled (because as a hacky way of doing "AJAX" it sets the voting url as the src value of an <img> tag that doesn't actually get displayed).