Correct, a copy of a face-down 2/2 creature is also a 2/2 creature.
A copy effect can only ever copy what's visible to all players. Any characteristics of an object that are not visible to all players can have no effect on gameplay, unless they are revealed to everyone before or as they affect the gameplay.
707.2a If a face-up permanent is turned face down by a spell or ability that doesn't list any characteristics for that object, it becomes a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost. A permanent that enters the battlefield face down also has these characteristics unless otherwise specified by the effect that put it onto the battlefield face down or allowed it to be cast face down. These values are the copiable values of that object's characteristics.