Next time you process a chicken gizzard, slice it open and take a look at the inside. You may well find grit inside, and if you rinse it and massage the inside you probably will work grit out of it.
The crop stores the food a chicken gobbles down, and the real grinding of food happens inside the gizzard. The grit gets trapped in the folds of muscle inside the gizzard, and as food (grain) works it's way into the gizzard from the crop, it is ground up into a form that the chicken's intestines can break down further and digest.
Birds have a completely different metabolism and digestive system from mammals, and it is fascinating and important to understand how their metabolism functions, so that you can provide them with the proper nutrition, understand what makes an unsanitary coop and what to do about it, as well as being able to look at the poop you are cleaning out of the coop every day and know if your birds are healthy or not.
In general, if the chooks have access to grit they will eat enough to keep their gizzards well equipped for grinding. In my covered run the floor is sand over gravel, and the chooks eat out there. I'm pretty sure that any excess sand they may eat passes harmlessly through their system.
Great question that does not have a simple answer, and I'm glad you asked!