Providing students with flexible and timely academic support is a challenge at most colleges and universities, leaving many students without help outside scheduled hours. Large language models (LLMs) are promising for bridging this gap, but interactions between students and LLMs are rarely overseen by educators. We developed and studied an LLM-powered course assistant deployed across multiple computer science courses to characterize real-world use and understand pedagogical implications. By Spring 2024, our system had been deployed to approximately 2,000 students across six courses at three institutions. Analysis of the interaction data shows that usage remains strong in the evenings and nights and is higher in introductory courses, indicating that our system helps address temporal support gaps and novice learner needs. We sampled 200 conversations per course for manual annotation: most sampled responses were judged correct and helpful, with a small share unhelpful or erroneous; few responses included dedicated examples. We also examined an inquiry-based learning strategy: only around 11% of sampled conversations contained LLM-generated follow-up questions, which were often ignored by students in advanced courses. A Bloom's taxonomy analysis reveals that current LLM capabilities are limited in generating higher-order cognitive questions. These patterns suggest opportunities for pedagogically oriented LLM-based educational systems and greater educator involvement in configuring prompts, content, and policies.