Hi,
You could create a custom field of the table "order" via the menu Display>Custom fields. It would appear during the checkout so your customers could enter it at that point and it would be stored with the order.
Of course, this is just informational. It won't automatically send notification emails of the order to that email address.
You would have to edit he emails via the menu System>Emails and add such code at the end of the preload area of your order notification emails:
$order->customer->user_email = $order->XXX;
where XXX would be the column name of your custom field.
This would require the Business edition.