Large Language Models (LLMs), when paired with prompt-based tasks, have significantly reduced data annotation costs and reliance on human annotators. However, evaluating the quality of their annotations remains challenging in dynamic, unsupervised environments where oracle feedback is scarce and conventional methods fail. To address this challenge, we propose a novel agentic annotation paradigm, where a student model collaborates with a noisy teacher (the LLM) to assess and refine annotation quality without relying on oracle feedback. The student model, acting as an unsupervised feedback mechanism, employs a user preference-based majority voting strategy to evaluate the consistency of the LLM outputs. To systematically measure the reliability of LLM-generated annotations, we introduce the Consistent and Inconsistent (CAI) Ratio, a novel unsupervised evaluation metric. The CAI Ratio not only quantifies the annotation quality of the noisy teacher under limited user preferences but also plays a critical role in model selection, enabling the identification of robust LLMs in dynamic, unsupervised environments. Applied to ten open-domain NLP datasets across four LLMs, the CAI Ratio demonstrates a strong positive correlation with LLM accuracy, establishing it as an essential tool for unsupervised evaluation and model selection in real-world settings.