It probably does. It'll take me a while to dig through the source to find the cause, but preliminary evidence suggests that fastcgi_cache_key doesn't handle $cookie_* variables correctly. If the cookie doesn't exist, it seems to result in a unique key every time. (Edit: The workaround is to assign the $cookie_* variable to another variable and then use that in fastcgi_cache_key.)
If anyone is curious what sort of increase in traffic you should expect from a link to your site appearing on HN, we're getting about 230 additional backend requests per second--that doesn't include anything cached by Cloudflare. You can monitor it in realtime here: https://www.nameprosstatus.com/