None of my eggs are ever refrigerated unless they are really dirty and I wash them. If left unwashed they can sit on the counter for 2 weeks. That's the generally accepted rule. Unless you read the FDA website, then they will scare you into refrigerating everything.
But, no, fertile eggs will not start developing at normal room temp. The majority of my eggs are fertile and after storing them on the counter for over a year, I have yet to find an inedible egg.
