You won't want to count on these invitations leaving the web, either. A WhatsApp spokesperson asserted these links were shared in "searchable, public channels," and that people who want to keep links private shouldn't share them on publicly reachable sites. Google's public search liaison, Danny Sullivan, reiterated this by saying it was "no different" than any other situation where sites allow links to be publicly listed. He added that Google offers tools to block content from being listed. A Google spokesperson didn't have more to add following an inquiry from Engadget.
Concerns appear to have been circulating since at least November 2019, when a Facebook representative told one user that this was an "intentional product decision."
This should mean that it's possible to keep private chats truly closed off by asking members to avoid sharing invitations in public spaces. The problem, of course, is that it only takes one not-so-careful participant to make a link public, and users might not always understand when sharing a link makes it visible in search engines. It also undermines Facebook's assertion that its future is private -- it's hard to maintain privacy if a link shared in one place is visible to anyone with a knack for Google searches.