Recent advances in artificial intelligence (AI) have shown promise in automating key aspects of Agile project management, yet their impact on team cognition remains underexplored. In this work, we investigate cognitive offloading in Agile sprint planning by conducting a controlled, three-condition experiment comparing AI-only, human-only, and hybrid planning models on a live client deliverable at a mid-sized digital agency. Using quantitative metrics -- including estimation accuracy, rework rates, and scope change recovery time -- alongside qualitative indicators of planning robustness, we evaluate each model's effectiveness beyond raw efficiency. We find that while AI-only planning minimizes time and cost, it significantly degrades risk capture rates and increases rework due to unstated assumptions, whereas human-only planning excels at adaptability but incurs substantial overhead. Drawing on these findings, we propose a theoretical framework for hybrid AI-human sprint planning that assigns algorithmic tools to estimation and backlog formatting while mandating human deliberation for risk assessment and ambiguity resolution. Our results challenge the assumption that efficiency equates to effectiveness, offering actionable governance strategies for organizations seeking to augment rather than erode team cognition.