Binary classification using images and an external dataset
Yes you can most certainly combine the two ways of information in CNNs.
Let's take a look at a CNN:

Roughly speaking, CNNs consist of two parts:

one that has convolutional layers and optinally pooling ones
and one that has fully connected layers.

The first is used for extracting features from the image, while the second is used for using these extracted features to classify the image. The last part essentially is like a regular fully-connected Neural Network.
If you want to add more information to the CNN, which is not an image, you can add this to the first fully connected layer of the network. This way this information bypasses the feature extraction step (which is relevant only for imaging data) and is used only for classification.