Apple generally ships parts overnight to shops. I've worked somewhere that had an AASP as part of it. Occasionally there's a delay but around 90% of the time our guys could order up to about 4PM EST and have it come in for the midday FedEx Express dropoff the next day. And this wasn't in a major metro area where overnight delivery is common/easy.

2-3 days would have been a plausible turnaround time. 7 is laziness or a long queue.