Instead of using this small hack consider using this plugin https://github.com/devgeniem/wp-core-blocker. It takes care of much more edge cases and core functionality.

disable-updates-and-external-connections.php

<?php
/**
 * Plugin Name: Disable All Updates and External Connections
 * Description: Plugin which disables core, plugin and theme updates and connections to wordpress.org This is quite useful in local development
 * Version: 1.0.0
 * Author: Onni Hakala
 * Author URI: https://github.com/onnimonni
 * License: MIT License
 */

namespace geniem\helper;

use stdClass;

/**
 * Contains small snippets to disable
 */
class DisableUpdatesAndConnections {

    /**
     * Activate hooks into wordpress
     */
    static function init() {

        // Tell wordpress that everything is just fine
        add_filter( 'pre_site_transient_update_core', array( __CLASS__, 'current_core_theme_and_plugins_are_just_fine' ) );
        add_filter( 'pre_site_transient_update_plugins', array( __CLASS__, 'current_core_theme_and_plugins_are_just_fine' ) );
        add_filter( 'pre_site_transient_update_themes', array( __CLASS__, 'current_core_theme_and_plugins_are_just_fine' ) );

        // Disable wp-cron update checks
        wp_clear_scheduled_hook( 'wp_version_check' );
        wp_clear_scheduled_hook( 'wp_update_plugins' );
        wp_clear_scheduled_hook( 'wp_update_themes' );

        // Remove admin news dashboard widget
        add_action( 'admin_init', array( __CLASS__, 'remove_dashboards' ) );

        // If user didn't define these few core variables we add them now
        if ( ! defined( 'WP_AUTO_UPDATE_CORE' ) ) {
            define( 'WP_AUTO_UPDATE_CORE', false );
        }

        if ( ! defined( 'WP_HTTP_BLOCK_EXTERNAL' ) ) {
            define( 'WP_HTTP_BLOCK_EXTERNAL', true );
        }
    }

    /**
     * Always returns information that current version is okay.
     * This way wordpress doesn't make additional requests to wordpress.org
     * and we dictate updating process always
     */
    static function current_core_theme_and_plugins_are_just_fine() {
        global $wp_version;
        $current = new stdClass();

        // wp-includes/update.php:604 _maybe_update_core() checks these two variables
        // wp-includes/update.php:627 _maybe_update_plugins() checks only last_checked
        // wp-includes/update.php:643 _maybe_update_themes() checks only last_checked
        $current->version_checked = $wp_version;
        $current->last_checked = time();

        return $current_core;
    }

    /**
     * Remove WordPress news dashboard widget
     */
    static function remove_dashboards() {
        remove_meta_box( 'dashboard_primary', 'dashboard', 'normal' );
    }
}

DisableUpdatesAndConnections::init();