We evaluate access to a course-integrated generative AI (GenAI) tutor in a randomized controlled trial involving 2,379 undergraduate students and 30 instructors across multiple disciplines in a large U.S. public university. Among sections of the same course, tutor access reduced final grades by 0.37 standard deviations and learning management system participation by 0.90 standard deviations. Participation declines were similarly large in the full sample, and estimated academic losses were greater among first-generation students. These findings suggest that introducing an AI tutor may displace engagement with existing learning activities without improving academic performance, with potentially differential impact across student groups.