Yes. If the admin page is not blocked by robots.txt and is linked publicly, Google can index it. Use site:example.com inurl:admin to check.
Introduction In the world of web development, cybersecurity, and penetration testing, one of the most common yet critical challenges is locating the hidden entrance to a website’s command center: the administrator login page . Whether you are a website owner who has lost access to your admin panel, a security auditor testing for vulnerabilities, or a developer managing multiple CMS installations, the question remains the same: Where is the admin login page? admin login page finder link
find_admin_pages(sys.argv[1], sys.argv[2]) and penetration testing