Spiking Neural Networks (SNNs) have attracted growing interest in both computational neuroscience and artificial intelligence, primarily due to their inherent energy efficiency and compact memory footprint. However, achieving adversarial robustness in SNNs, (particularly for vision-related tasks) remains a nascent and underexplored challenge. Recent studies have proposed leveraging sparse gradients as a form of regularization to enhance robustness against adversarial perturbations. In this work, we present a surprising finding: under specific architectural configurations, SNNs exhibit natural gradient sparsity and can achieve state-of-the-art adversarial defense performance without the need for any explicit regularization. Further analysis reveals a trade-off between robustness and generalization: while sparse gradients contribute to improved adversarial resilience, they can impair the model's ability to generalize; conversely, denser gradients support better generalization but increase vulnerability to attacks. Our findings offer new insights into the dual role of gradient sparsity in SNN training.