In the case of the quick shop, it makes even more sense to have a generator so that other stuff can be sold too.
If the employees are trained there is no reason they can't stay open without power.
The key being training.
Most of the supermarkets I work at will have manual credit card machines and slips buried under each registrar but I doubt many folks know how to use them.
Small business owners are generally smart enough to figure out what is worth spending money on and what is not. I think the lack of generators at gas stations and convenience stores is a pretty good indicator that they are not worth it.
Even the large chain supermarkets I work in will generally only have enough generator capacity to run the required lighting along with the point of sale equipment, scales, telephones and PA systems. The refrigeration will not be included. That gives them about a 3 to 4 hour window before product starts to go south.
If it looks like the outage will go longer they will plastic in the open cases, put dry ice in the coolers and call us to hook up a large portable unit.