Custom submit handlers don't play nicely with "One page profile"

If "Cookie cache bypass" is enabled, "One page profile" will not work. I hope I will be able to provide more details after code review.

The code of "Cookie cache bypass":

function cookie_cache_bypass_form_alter(&$form, $form_state, $form_id) {
  $form['#submit'][] = 'cookie_cache_bypass_submit';
}

function cookie_cache_bypass_submit() {
  global $cookie_domain;
  $lifetime = variable_get('cache_lifetime', 300);
  setcookie('NO_CACHE', 'Y', $_SERVER['REQUEST_TIME'] + ($lifetime + 300), '/', $cookie_domain);
}