Hospital administration departments handle a wide range of operational tasks and, in large hospitals, process over 10,000 requests per day, driving growing interest in LLM-based automation. However, prior work has focused primarily on patient-physician interactions or isolated administrative subtasks, failing to capture the complexity of real administrative workflows. To address this gap, we propose H-AdminSim, a comprehensive simulation framework that combines realistic data generation with multi-agent-based simulation of hospital administrative workflows. These tasks are quantitatively evaluated using detailed rubrics, enabling systematic comparison of LLMs. Through FHIR integration, H-AdminSim provides a unified and interoperable environment for testing administrative workflows across heterogeneous hospital settings, serving as a standardized testbed for assessing the feasibility and performance of LLM-driven administrative automation.