sitemap.xml for auth sites

You can't make an user/password, that would be a security hole. And they don't even pick up on that.
What you need to to is look for a googlebot user agent, and verify it's origin. And let that bot inside without username/password.

https://support.google.com/webmasters/an...0553?hl=en

So, it will be semi-public.

If Google starts crawling those pages (you got Google Search Console right?) you should see those urls failing. You should return a correct header for Google and other bots if they find a page that require login. Like 403. If you return 200, they will think it's the correct content showing up.

So, I create an account for Googlebot in my auth system(I make up an email and a password). 
Should I then do something like this in MY_Controller: (code updated)

PHP Code:

// Only check if  not logged in users are a google bot
if(!$this->ion_auth->logged_in()) {    
    // Verify if caller is a google bot
    $remote_ip = $_SERVER['REMOTE_ADDR'];
    $domain = gethostbyaddr($remote_ip);
    if (in_array($domain, ['googlebot.com', 'google.com']) && gethostbyname($domain) == $remote_ip) {
        // Caller is a google bot, login the caller and redirect to some logged_in page where the "inside" crawl can start...
        $this->ion_auth->login('made_up_email', 'made_up_password');
        redirect('auth/logged_in_start');
    } 
} 
// Run script...