Studies on in-vehicle conversational agents have traditionally relied on pre-scripted prompts or limited voice commands, constraining natural driver-agent interaction. To resolve this issue, the present study explored the potential of a ChatGPT-based in-vehicle agent capable of carrying continuous, multi-turn dialogues. Forty drivers participated in our experiment using a motion-based driving simulator, comparing three conditions (No agent, Pre-scripted agent, and ChatGPT-based agent) as a within-subjects variable. Results showed that the ChatGPT-based agent condition led to more stable driving performance across multiple metrics. Participants demonstrated lower variability in longitudinal acceleration, lateral acceleration, and lane deviation compared to the other two conditions. In subjective evaluations, the ChatGPT-based agent also received significantly higher ratings in competence, animacy, affective trust, and preference compared to the Pre-scripted agent. Our thematic analysis of driver-agent conversations revealed diverse interaction patterns in topics, including driving assistance/questions, entertainment requests, and anthropomorphic interactions. Our results highlight the potential of LLM-powered in-vehicle conversational agents to enhance driving safety and user experience through natural, context-rich interactions.