If you send it in a normal mailing envelope, you will need to put plenty of bubble wrap or something in it to make it too thick to go through the machines. If not, the game could possibly be lost or damaged by the machines. I have had both happen to me before.
I would have it in the mail within 36 hours of bidding's end. And in saying 36 hours that would be an extreme. Sort of a CMA. (cover my ...) sound okay? :) only children and emergencies could get in the way of swift action.....they do so regularly. :)