This paper investigates the adversarial robustness of Deep Neural Networks (DNNs) using Information Bottleneck (IB) objectives for task-oriented communication systems. We empirically demonstrate that while IB-based approaches provide baseline resilience against attacks targeting downstream tasks, the reliance on generative models for task-oriented communication introduces new vulnerabilities. Through extensive experiments on several datasets, we analyze how bottleneck depth and task complexity influence adversarial robustness. Our key findings show that Shallow Variational Bottleneck Injection (SVBI) provides less adversarial robustness compared to Deep Variational Information Bottleneck (DVIB) approaches, with the gap widening for more complex tasks. Additionally, we reveal that IB-based objectives exhibit stronger robustness against attacks focusing on salient pixels with high intensity compared to those perturbing many pixels with lower intensity. Lastly, we demonstrate that task-oriented communication systems that rely on generative models to extract and recover salient information have an increased attack surface. The results highlight important security considerations for next-generation communication systems that leverage neural networks for goal-oriented compression.