Last week, when we stayed at SSR, we had groceries delivered from Disney. We checked in at noon, we were able to get into our room right away, and when we returned at dinner time to change clothes, our groceries had been delivered, and were put in the fridge and freezer. We also did online check in, (tho' we spent a lot of time at the counter, including being given a choice of a couple of rooms, but that's another story). Not sure how a late night check in would work. It looked like they may have gone to the store to purchase the items we ordered (they included the register receipt), and since the store closes at 11 they may have to wait until the morning to purchase your groceries. I'm sure you could call and ask them.
Yes, we could have ordered (and have in the past) from Garden Grocer, but we only ordered a few items, and when I comparison priced, the Disney prices weren't that higher.