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Automated classroom engagement recognition holds substantial promise for scalable learning analytics, yet the suitability of modern Vision-Language Models (VLMs) for this task under zero-shot conditions remains largely unexplored. We present a systematic benchmark that evaluates five widely-used VLMs: CLIP, BLIP-VQA, GPT-4o, LLaVA-1.5-7B, and Qwen2.5VL-7B-Instruct across two complementary educational datasets: DAiSEE, an individual-student video dataset (300 sampled test clips), and the Student Classroom Behaviour dataset (SCB, 1,168 scene-level images). Each model is probed with three prompt variants spanning minimal, rubric-anchored, and chain-of-thought designs. Our experiments reveal three primary failure modes of zero-shot VLMs for engagement recognition: (1) near-random performance on individual students, with Cohen's kappa never exceeding 0.10 on DAiSEE; (2) severe class collapse, where models assign 85-100% of predictions to a single engagement level regardless of visual content; and (3) extreme prompt sensitivity, with accuracy swings of up to 32 percentage points on identical images depending solely on prompt phrasing. Remarkably, scene-level classification on SCB is substantially more tractable: CLIP and GPT-4o achieve kappa approximately 0.60 when prompted with behaviorally-grounded rubrics. We also document a practical barrier for deployment: GPT-4o's safety filters reject 98% of chain-of-thought requests involving individual student faces. Our findings provide a calibrated baseline and surface critical design considerations for the use of VLMs in educational observation systems.