Deep learning based automatic modulation classification (AMC) has received significant attention owing to its potential applications in both military and civilian use cases. Recently, data-driven subsampling techniques have been utilized to overcome the challenges associated with computational complexity and training time for AMC. Beyond these direct advantages of data-driven subsampling, these methods also have regularizing properties that may improve the adversarial robustness of the modulation classifier. In this paper, we investigate the effects of an adversarial attack on an AMC system that employs deep learning models both for AMC and for subsampling. Our analysis shows that subsampling itself is an effective deterrent to adversarial attacks. We also uncover the most efficient subsampling strategy when an adversarial attack on both the classifier and the subsampler is anticipated.