Federated learning (FL) allows collaborative model training across healthcare sites without sharing sensitive patient data. However, real-world FL deployment is often hindered by complex operational challenges that demand substantial human efforts. This includes: (a) selecting appropriate clients (hospitals), (b) coordinating between the central server and clients, (c) client-level data pre-processing, (d) harmonizing non-standardized data and labels across clients, and (e) selecting FL algorithms based on user instructions and cross-client data characteristics. However, the existing FL works overlook these practical orchestration challenges. These operational bottlenecks motivate the need for autonomous, agent-driven FL systems, where intelligent agents at each hospital client and the central server agent collaboratively manage FL setup and model training with minimal human intervention. To this end, we first introduce an agent-driven FL framework that captures key phases of real-world FL workflows from client selection to training completion and a benchmark dubbed FedAgentBench that evaluates the ability of LLM agents to autonomously coordinate healthcare FL. Our framework incorporates 40 FL algorithms, each tailored to address diverse task-specific requirements and cross-client characteristics. Furthermore, we introduce a diverse set of complex tasks across 201 carefully curated datasets, simulating 6 modality-specific real-world healthcare environments, viz., Dermatoscopy, Ultrasound, Fundus, Histopathology, MRI, and X-Ray. We assess the agentic performance of 14 open-source and 10 proprietary LLMs spanning small, medium, and large model scales. While some agent cores such as GPT-4.1 and DeepSeek V3 can automate various stages of the FL pipeline, our results reveal that more complex, interdependent tasks based on implicit goals remain challenging for even the strongest models.