I’d imagine it would just affect the amount of time that the eggs remain healthful – if you eat a lot of eggs, it’s probably better to buy fresh ones (ie look at the dates on the carton) and keep them out, they generally cook better from room temperature than cold.
Also you can keep eggs fresher with sealants – like wax coatings on the shell or plastic air-proof sealing around them..or those dirt-packings or whatever.
Either way, I keep mine in the fridge most of the time, and take what I want out a few hours in advance, rather be safe than end up with salmonella in China 😀