when is wp_loaded initiated

hi all
when is wp_loaded initiated?
1.when admin enter the site or not?
2.when user enter the site or not?

I use this script:

// add update check when admin login
if (is_admin()) {
	function wp_plugin_update() {
			include( plugin_dir_path( __FILE__ ) . 'wp-plugin-update.php');
	}
	add_action( 'admin_init', 'wp_shabbat_update' );
}
// add update check when user enter the site after footer loaded
if (!(is_admin() )) {
    function wp_plugin_update() {
		include( plugin_dir_path( __FILE__ ) . 'wp-plugin-update.php');
		}
	add_action( 'wp_loaded', 'wp_plugin_update' );
}

can I only use this and it will work with admin and when user enter the site? :

function wp_plugin_update() {
		include( plugin_dir_path( __FILE__ ) . 'wp-plugin-update.php');
		}
add_action( 'wp_loaded', 'wp_plugin_update' );