It depends on the species of crayfish. Larger species such as P. clarkii, P. aleni, or any of the Cherax species (I currently have C. quadricarinatus), will eat snails. It does not matter if the snail has a trap door or not. They'll use their claws to break the shell open to get to the snail meat.
I frequently take a bunch of MTS out of my shrimp tanks and put them in with my crayfish, he really enjoys eating them.