Do studies of visual illusion demonstrate the importance of conceptually driven processes?

In a word, yes. Conceptually driven processing is also referred to as top-down processing. It refers to the dependence on prior knowledge or our expectations concerning the incoming stimulation. An example of when conceptually driven processes are in action is when we see a face. Once the image has entered the eye our previous built up knowledge of human faces can guide us into actually recognising the image as a face. Therefore conceptually driven processes uses a higher level of conceptual processes which include such things as memories of past experiences, general organisational strategies, knowledge of the world and expectations based upon the surrounding context or situation Coren, Porac and Ward (1978)….(short extract)