I have a sourdough pancake recipe with eggs that sits out overnight. Not had a problem. The biggest threat from eggs may be salmonella. If you don't cross-contaminate anything with the raw dough, cooking should kill the salmonella.
In most parts of the world, eggs are stored at room temperature. In the U.S., health regs require producers to wash the eggs; this may remove any pathogens from the outside of the egg, but it also removes a protective layer - necessitating refrigeration. Still, for many years, wholesalers and retailers stored washed eggs at room temp.
Disclaimer: I'm not a professional. If you have any doubts about the safety of anything, don't take the advice of strangers.