Excellent answer, shaldna. I don't dispute an part of it.
I happen to shop at a the flagship store consistently rated as the US's best grocery store chain. (Luck of the draw, location-wise--but damn, other stores suck in comparison.) When the power goes out briefly, the shopping floor has minimal lighting. The refrigerator cases, beer cooler, and deli do not have back-up power from the generator. I'm not sure if the freezer cases do. However, the storage portion shoppers never see is all kept at the proper temperature, since a great deal more stock is there than on the shopping floor.
When the power is off for an extended period, which has happened twice while I've lived here, more of the shopping floor is served by the generators, so the shopping experience is very nearly normal. Obviously this depends on a decision (probably by corporate) to use additional generators and to get them up and running. It's usually at least 24 hours after the power goes before this happens--and this is at a great store which is making serious profits.
So in your fiction, are there people who have the authority and capability of getting more generators fueled and the power they produce to the parts of the store that were not considered important enough to instantly be powered by the main generator? If there's something catastrophic going on, employees will not put the store's needs first.
Ask to talk to the store manager where you shop. Tell him or her you're a writer and want to get a detail right, and see if s/he'll talk to you then and there, or make time for you at his or her convenience.
Maryn, shy but not scared of grocery store managers