Absolutely 100% Yes, do put eggshells in your compost with abandon. Even if you a full time egg eater, they will only ever be a tiny component anyway.
Eggshells are just good old calcium carbonate crystal in a firm glue of protein that breaks down without a fuss.
Calcium is an essential plant nutrient & is great for acidic soil.
Soils that already have a lot of calcium, like chalky soil, don't need it, but if you are growing plants that like that high pH soil, it makes no difference.
If you are fanatically struggling to lower the pH of your soil (make it more acidic), lose the eggshells and make sure all your coffee grounds & citrus peel ends up on the heap, but really, you'd have to be an omlette addict with your own hens to get through enough eggshells to make any measureable difference.
Egg boxes make great free seedling trays - when they are ready for planting out, just separate the segments and maybe pinch out the bottom of each little pocket and put it straight into the soil.
Have fun and enjoy those eggs,