Couldn't make it to the 2-hour mark before bumping, huh?
There is a defined timeline which I can't remember exactly but which you can get by calling Apple. I recently picked up two new computers that were arriving on different days. I think I was told that if the machine came into the store on Monday or Tuesday, they wanted it picked up by Sunday.
But when I called the specific store itself, they told me they didn't go by such a stringent deadline and wouldn't cancel the order and return the shipment without reaching out to the customer first.
So, in answer to your question, there is a finite, defined schedule put forth by the corporate office, but your mileage really depends on the policies of the specific store receiving the shipment.