No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of *locality*, i.e. small changes in input lead to small changes at hidden layer. This is a nice property because it means the mapping is not too sensitive, which should help it generalise beyond the training data.

(There is an extra complication: the CAE tries in particular to enforce locality *along the direction of the low-dimensional manifold* which all autoencoders assume is present in the input data. I find this part a bit harder to explain.)