State-of-the-art large language models (LLMs) show high performance in general visual question answering. However, a fundamental limitation remains: current architectures lack the native 3D spatial reasoning required for direct analysis of volumetric medical imaging, such as CT or MRI. Emerging agentic AI offers a new solution, eliminating the need for intrinsic 3D processing by enabling LLMs to orchestrate and leverage specialized external tools. Yet, the feasibility of such agentic frameworks in complex, multi-step radiological workflows remains underexplored. In this work, we present a training-free agentic pipeline for automated brain MRI analysis. Validating our methodology on several LLMs (GPT-5.1, Gemini 3 Pro, Claude Sonnet 4.5) with off-the-shelf domain-specific tools, our system autonomously executes complex end-to-end workflows, including preprocessing (skull stripping, registration), pathology segmentation (glioma, meningioma, metastases), and volumetric analysis. We evaluate our framework across increasingly complex radiological tasks, from single-scan segmentation and volumetric reporting to longitudinal response assessment requiring multi-timepoint comparisons. We analyze the impact of architectural design by comparing single-agent models against multi-agent "domain-expert" collaborations. Finally, to support rigorous evaluation of future agentic systems, we introduce and release a benchmark dataset of image-prompt-answer tuples derived from public BraTS data. Our results demonstrate that agentic AI can solve highly neuro-radiological image analysis tasks through tool use without the need for training or fine-tuning.