The utilization of compressive sensing (CS) techniques for hyperspectral (HS) imaging is appealing since HS data is typically huge and very redundant. The CS design offers a significant reduction of the acquisition effort, which can be manifested in faster acquisition of the HS datacubes, acquisition of larger HS images and removing the need for postacquisition digital compression. But, do all these benefits come at the expense of the ability to extract targets from the HS images? The answer to this question, of course, depends on the specific CS design and on the target detection algorithm employed. In a previous study we have shown that there is virtually no target detection performance degradation when a classical target detection algorithm is applied on data acquired with CS HS imaging techniques of the kind we have developed during the last years. In this paper we further investigate the robustness of our CS HS techniques for the task of object classification by deep learning methods. We show preliminary results demonstrating that deep neural network classifiers perform equally well when applied on HS data captured with our compressively sensed methods, as when applied on conventionally sensed HS data.