Deliberation is essential to well-functioning democracies, yet physical, economic, and social barriers often exclude certain groups, reducing representativeness and contributing to issues like group polarization. In this work, we explore the use of large language model (LLM) personas to introduce missing perspectives in policy deliberations. We develop and evaluate a tool that transcribes conversations in real-time and simulates input from relevant but absent stakeholders. We deploy this tool in a 19-person student citizens' assembly on campus sustainability. Participants and facilitators found that the tool sparked new discussions and surfaced valuable perspectives they had not previously considered. However, they also noted that AI-generated responses were sometimes overly general. They raised concerns about overreliance on AI for perspective-taking. Our findings highlight both the promise and potential risks of using LLMs to raise missing points of view in group deliberation settings.