No it shouldn’t affect the menu. If you want to test it, you can look in your front-page.php file and remove/comment this out to see what happens –
//* Enqueue parallax script
add_action( 'wp_enqueue_scripts', 'aspire_enqueue_parallax_script' );
function aspire_enqueue_parallax_script() {
if ( ! wp_is_mobile() ) {
wp_enqueue_script( 'parallax-script', get_bloginfo( 'stylesheet_directory' ) . '/js/parallax.js', array( 'jquery' ), '1.0.0' );
}
}
You’ll probably need to remove the fixed background for that particular widget to see if that makes a difference.