I grew up around a lot of Amish (in Delaware) and as one poster already mentioned, they do use them but often do not take care of them and are often not used regularly.

It's common to find extremely rusted examples of old rifles or shotguns stuffed in barns or basements.

IN PA, They often buy them at private auctions that don't run pics or most often FTF since many do not have ID, or they sometimes use air rifles for critter control.