Eating disorders (ED) are complex mental health conditions that require long-term management and support. Recent advancements in large language model (LLM)-based chatbots offer the potential to assist individuals in receiving immediate support. Yet, concerns remain about their reliability and safety in sensitive contexts such as ED. We explore the opportunities and potential harms of using LLM-based chatbots for ED recovery. We observe the interactions between 26 participants with ED and an LLM-based chatbot, WellnessBot, designed to support ED recovery, over 10 days. We discovered that our participants have felt empowered in recovery by discussing ED-related stories with the chatbot, which served as a personal yet social avenue. However, we also identified harmful chatbot responses, especially concerning individuals with ED, that went unnoticed partly due to participants' unquestioning trust in the chatbot's reliability. Based on these findings, we provide design implications for safe and effective LLM-based interventions in ED management.