Security operations centers (SOCs) face a persistent challenge: efficiently triaging a high volume of user-reported phishing emails while maintaining robust protection against threats. This paper presents the first randomized controlled trial (RCT) evaluating the impact of a domain-specific AI agent - the Microsoft Security Copilot Phishing Triage Agent - on analyst productivity and accuracy. Our results demonstrate that agent-augmented analysts achieved up to 6.5 times as many true positives per analyst minute and a 77% improvement in verdict accuracy compared to a control group. The agent's queue prioritization and verdict explanations were both significant drivers of efficiency. Behavioral analysis revealed that agent-augmented analysts reallocated their attention, spending 53% more time on malicious emails, and were not prone to rubber-stamping the agent's malicious verdicts. These findings offer actionable insights for SOC leaders considering AI adoption, including the potential for agents to fundamentally change the optimal allocation of SOC resources.