Depends on the business doesn't it?
Some won't be allowed to open as they won't be insured if no power for heating, lighting and security systems. Workplaces aren't safe for staff if there's no power for lighting potentially dark/gloomy storerooms, back rooms, toilets/kitchens, etc. Likewise if no heating, the workplace may be too cold for staff to legally be required to work.
Of course, some smaller businesses can open based on natural light if they have lots of windows.
Likewise if they have their own generators they can open.
We did indeed have a local shop which opened during Storm Desmond, but soon had to close as they sold out of the stock they could sell (they couldn't sell fresh/frozen stock as the fridges/freezers were down so the stock melted or warmed too much, hence unsafe to sell).
Owner-managed small shops will be better placed to stay open temporarily as they're more likely to be able to rely on memory for prices and able to work out sums of shopping and change without need of a till system - staff are less likely to be able to work without electronic POS tills etc. Workplace H&S legislation is less of a problem if it's the business owner working in the shop without power, rather than employees where it may be against employment law for them to be expected to work in what are almost certainly unsafe conditions.
But back to the point of this thread i.e. Starbucks, I think it's highly unlikely that a chain like Starbucks would open in a blackout due to the insurance, power, heating, security and staffing problems.