How close the admin overlay on submit for a drupal form shown within the admin overlay
I don't have experience with the admin overlay, but from what you are writing, I understand that you want to add the class "overlay-close" to an element (admin overlay?) when submit button is pressed. You can adapt the following code for that:

$('#form_id').submit(function(){
  // Add "overlay-close" class to the proper element
  $('#element').addClass('overlay-close');
});