The check reads what the server answers for the URL: the status of every response, the Location of each redirect, the X-Robots-Tag headers and, for an HTML page, the robots and googlebot meta tags in its first megabyte. A tag inside a comment, a script, a style block or a template does not count. A directive addressed to another crawler, such as bingbot: noindex, is listed in robots.header and not counted. A PDF or an image is judged on its headers alone.
Left out on purpose: robots.txt rules, canonical tags, meta-refresh redirects and rel="nofollow" on single links. nofollow here is the page-wide directive.
Whether a page is already in Google's index is a different question, and the Google Index Checker API answers it. Once a page can be indexed, the Link Indexing API submits it for crawling.