Updates the `blog_public` option for a given site ID.

function wp_update_blog_public_option_on_site_update( $site_id, $public ) {

	// Bail if the site's database tables do not exist (yet).
	if ( ! wp_is_site_initialized( $site_id ) ) {
		return;
	}

	update_blog_option( $site_id, 'blog_public', $public );
}