Yes. Eggshells compost, but far more slowly than almost anything else you will add. Expect to still find recognisable fragments a year later. Crush them and it stops being a problem. Below: whether you can compost eggshells, why, how much to add, and the mistakes that cause trouble.
Adding eggshells to a pile. Chop it, mix it, bury it.
Why
Eggshell is about 95% calcium carbonate, a mineral. Microbes break down organic matter; they have very little to do with a mineral shell. What actually breaks eggshells down is physical abrasion and slow chemical weathering in acidic conditions.
The calcium is genuinely useful in soil, and it does become available eventually. Just on a timescale of years rather than months.
How to add it
Crush them. Dried shells crumbled by hand are fine; blitzed to powder in a blender is better and disappears in a single season. Whole shells will still be whole next spring.
There is no quantity limit worth worrying about. Nobody produces enough eggshell to unbalance a pile.
Common mistakes
Adding them whole and then concluding the pile is not working.
Expecting them to fix blossom end rot. That is a calcium uptake problem, usually caused by irregular watering. Adding calcium to soil that already has plenty does not solve it.
Worrying about salmonella. Rinse or dry them if it concerns you; in practice the risk in a garden compost pile is negligible.