That sounds really inconvenient (am I going to keep my food down there all the time, or is the plan to carry the entire contents of my refrigerator down there in an outage?) not terribly effective (RIP all the frozen stuff) and probably not any cheaper. Plus the hole can’t be used for other things like charging my phone.
Convert a chest freezer into refrigerator and you don't need batteries.
That's very smart and might end my quest for a truly quiet bedroom fridge, if it really only runs two minutes in an hour. (Light fridges marketed as "quiet" just produce near-constant annoying fan noise, quietly.)
If you own a house I'd look into very old school options like digging a deep hole to store your food in a dark&cool place - forgot the name for it but it'll work for weeks or months without a single milliwatt