We use Google's Custom Search API to provide search functionality for our website's users who want to search our website. Is there a way to include pages that are set to noindex via <meta name=robots content="follow, noindex"> in these search results? We do not want some of our pages (e.g. privacy policy) to be available through google SERPs but we do want them to show up in our internal search on our website. But since the internal search is implemented via Google's custom search API, "noindex pages" do not show up in the internal search.
Unfortunately, no.
Google's Programmable Search Engine has to follow the same rules as Google Search, and "noindex" means "do not show in search results" for both.