Graphical User Interface (GUI) agents adopt an end-to-end paradigm that maps a screenshot to an action sequence, thereby automating repetitive tasks in virtual environments. However, existing GUI agents are evaluated almost exclusively on commodity software such as Microsoft Word and Excel. Professional Computer-Aided Design (CAD) suites promise an order-of-magnitude higher economic return, yet remain the weakest performance domain for existing agents and are still far from replacing expert Electronic-Design-Automation (EDA) engineers. We therefore present the first systematic study that deploys GUI agents for EDA workflows. Our contributions are: (1) a large-scale dataset named GUI-EDA, including 5 CAD tools and 5 physical domains, comprising 2,000+ high-quality screenshot-answer-action pairs recorded by EDA scientists and engineers during real-world component design; (2) a comprehensive benchmark that evaluates 30+ mainstream GUI agents, demonstrating that EDA tasks constitute a major, unsolved challenge; and (3) an EDA-specialized metric named EDAgent, equipped with a reflection mechanism that achieves reliable performance on industrial CAD software and, for the first time, outperforms Ph.D. students majored in Electrical Engineering. This work extends GUI agents from generic office automation to specialized, high-value engineering domains and offers a new avenue for advancing EDA productivity. The dataset will be released at: https://github.com/aiben-ch/GUI-EDA.