Deep learning has been recently shown to improve performance in the domain of synthetic aperture sonar (SAS) image classification over existing shallow learning solutions. Given the constant resolution with range of a SAS, it is no surprise that deep learning techniques perform so well; the image of the seafloor produced by a SAS system is almost photographic in quality. Despite the image quality benefits of SAS, there is still room for classification improvement particularly in reducing the number of false alarms. This work addresses this by tackling one facet of the classification pipeline: image enhancement. Specifically, we ask and address the following question: Can we train a deep neural network to simultaneously enhance and classify a SAS image? We will respond in the affirmative as we introduce a new deep learning architecture tackling the problem, Data Adaptive Enhancement and Classification Network (DA-ECNet). DA-ECNet is a deep learning architecture which combines image enhancement as part of the classification procedure eliminating the need for a fixed state-of-the-art despeckling algorithm or enhancement module. Additionally, we train both image enhancement and classification jointly resulting in data adaptive image enhancement. Experiments on a challenging real-world dataset reveal that the proposed DA-ECNet outperforms state of the art deep learning as well as traditional feature based methods for SAS image classification.