If you eat a rotten egg it likely will not kill you but you will certainly or almost certainly become ill and may have a bad stomach ache, vomiting and diarrhea.
In some cases eating a rotten egg may also cause Salmonella Poisoning and you possibly could die but it's unlikely but it's still not worth the risk of eating a rotten egg.
Rotten eggs will also smell bad and when eggs are rotten they usually smell like Sulphur and would make you gag or vomit before you wanted to even eat it.
I've smelled rotten eggs before and there's no way I would want to eat it or even if I wanted to eat the rotten egg it would smell so bad that I would not be able to get it down my throat and that's a good thing.
If the rotten egg is bad and actually smells rotten do not cook it or eat it and instead throw it out.