Preheat oven to 350°.
Combine chocolate wafer crumbs and butter, tossing with a fork until well combined. Firmly press mixture into the bottom of a 9-inch springform pan coated with cooking spray. Bake at 350° for 10 minutes; cool completely.
Pour brewed coffee into a medium microwave-safe bowl. Sprinkle the gelatin over coffee; let stand 10 minutes. Combine cheeses and milk in a food processor; process until smooth. Microwave coffee mixture at HIGH for 20 seconds. Add coffee mixture to cheese mixture, and process until well combined. Pour cheese mixture into prepared crust. Cover and refrigerate overnight. Spread the whipped topping evenly over filling; sprinkle cocoa over pie. Chill 1 hour before serving.