The computed tomography imaging spectrometer (CTIS) is a snapshot hyperspectral imaging system. Its output is a 2D image of multiplexed spatiospectral projections of the hyperspectral cube of the scene. Traditionally, the 3D cube is reconstructed from this image before further analysis. In this paper, we show that it is possible to learn information directly from the CTIS raw output, by training a neural network to perform binary classification on such images. The use case we study is an agricultural one, as snapshot imagery is used substantially in this field: the detection of apple scab lesions on leaves. To train the network appropriately and to study several degrees of scab infection, we simulated CTIS images of scabbed leaves. This was made possible with a novel CTIS simulator, where special care was taken to preserve realistic pixel intensities compared to true images. To the best of our knowledge, this is the first application of compressed learning on a simulated CTIS system.