Most existing methods for Neural Architecture Search (NAS) focus on achieving state-of-the-art (SOTA) performance on standard datasets and do not explicitly search for adversarially robust models. In this work, we study the adversarial robustness of existing NAS architectures, comparing it with state-of-the-art handcrafted architectures, and provide reasons for why it is essential. We draw some key conclusions on the capacity of current NAS methods to tackle adversarial attacks through experiments on datasets of different sizes.