Yes, you can pre-crack eggs ahead of time i.e. a night before camping.    Pack the pre-cracked eggs in a water bottle or plastic bottle with a wide mouth, secure the lid, and put it in the refrigerator.    You can also use a Ziploc freezer bag to keep these pre-cracked eggs and freeze them.    Before leaving transfer the water bottle or Ziploc bag (whichever you have chosen to keep your cracked eggs in) into your cooler and surround it with ice packs or ice cubes to keep the eggs fresh and prevent any spoilage.