Convolutional neural networks (CNNs) are now predominant components in a variety of computer vision (CV) systems. These systems typically include an image signal processor (ISP), even though the ISP is traditionally designed to produce images that look appealing to humans. In CV systems, it is not clear what the role of the ISP is, or if it is even required at all for accurate prediction. In this work, we investigate the efficacy of the ISP in CNN classification tasks and outline the system-level trade-offs between prediction accuracy and computational cost. To do so, we build software models of a configurable ISP and an imaging sensor to train CNNs on ImageNet with a range of different ISP settings and functionality. Results on ImageNet show that an ISP improves accuracy by 4.6\%-12.2\% on MobileNets. Results from ResNets demonstrate these trends also generalize to deeper networks. An ablation study of the various processing stages in a typical ISP reveals that the tone mapper is the most significant stage when operating on high dynamic range (HDR) images, by providing 5.8\% average accuracy improvement alone. Overall, the ISP benefits system efficiency because the memory and computational costs of the ISP is minimal compared to the cost of using a larger CNN to achieve the same accuracy.