We did this on our last trip in April between VWL and BCV. When GG delivered the groceries, they had bags labeled as cold or frozen. When we moved, we just packed those items back into the bags and told the bellman which ones needed to stay cold. I was worried about things like ice cream for the switch, so we didn't order anything other than waffles that needed to be in the freezer, and they came out just fine. Bell services makes it very easy to move resorts.
TBH, I don't thing we'll do a split stay again if we are going to have groceries. It's enough work to pack up all 5 of our belongings, and have groceries to bag up as well. Plus with our moving, we had extra tips for each of the bell services people which added up. (We were slightly crazy this trip doing one night at CSR b/c we came in a day early, 2 nights at VWL and 5 nights at BCV). It was fine, but a lot of moving around, especially with three kids, one of which is an infant. Also, dh called bell services before I had all the groceries packed up so I was rushing to get everything ready. I ended up forgetting the things in the drawer in the fridge.
It's doable, and the cold things will stay cold. It's just a bit of a hassle if you have a lot of things.
