Yup, egg shell or oyster shell is a poor substitute for grit. The gizzard is actually pretty strong, and needs something hard to grind up the food with. Egg shells disintegrate within seconds in there. Something resembling sand in different sizes is your best bet. Or if you have some sandy dirt somewhere, that works too.
Like Fancy said, if they cut the grass themselves, you need not worry about crop impact. It's the stuff you cut up yourself that might cause problems. I've given the birds grass cuttings without issues though.
Some people can get away with it and I did for some time , then I lost my lovely BLRW pullet after I'd hand picked lush green grass for her.
It all comes down to soluable and non soluable grit, eggshells fall under the heading ' soluable ' she'll grit is insoluable , ie not absorbed by the body.