Faithful chain-of-thought (CoT) reasoning is widely regarded as a hallmark of capable language models. Yet its role in multi-turn interactive agents remains largely unexplored. We present the first systematic invesigation of action-level CoT faithfulness in multi-turn Large Language Model (LLM) agents, decomposing it into two interpretable and verifiable dimensions: consistency, which measures CoT-action alignment, and determinacy, which captures the degree to which CoT uniquely determines the selected action. We evaluate across Qwen family models of varying scales on Wordle tasks with increasing difficulty. Strikingly, simple inference-time resampling based on CoT faithfulness unlocks non-trivial performance from a zero baseline in weaker models, and yields gains of up to 30 ClemScore points in larger models, all without any additional training. However, our results reveal that faithfulness is not universally beneficial: its effectiveness is bounded by model capability and task difficulty, and jointly enforcing multiple dimensions may introduce competing constraints. These findings suggest that CoT faithfulness should not be viewed as an inherently beneficial property, but rather as a nuanced mechanism whose impact depends on when and how it is utilized in multi-turn agent reasoning.