After a few cycles, there is a high chance of finding an egg while exploring your surroundings. Critters naturally place eggs when they are happy, no matter if they are tamed or not.
After a few cycles, the eggs will hatch if left alone, and a new wild critter will appear. However, if the Storage Bin allows them, Duplicants will sweep the eggs and keep them away. But this is not the most efficient option for eggs.
Long answer short: No, eggs do not hatch in storage.
Putting eggs in storage will stop them from hatching. Instead, after ten cycles the eggs will crack and turn into Raw Egg and an Egg Shell.
The most efficient way to hatch an egg would be to place it in an Incubator and it will hatch in four cycles.
If that is not a viable option, then all eggs laid inside the stable and left alone will hatch in twenty cycles, so leaving them where they were found would be for the best.
Tip! To avoid turning all the eggs into omelets, reduce or stop the food production until all eggs have been looked after and accounted for.
The most effective way to acquire eggs would be to tame many critters and ensure they remain happy. This, however, can take a toll on your colony.
The skills necessary for ranching – Husbandry and Critter Ranching – take quite a while to train and acquire, therefore the best would be for a Duplicant to have an interest related to Husbandry.
Once the eggs have been successfully obtained, it is time to hatch them.