Large language models (LLMs) have the potential to aid and improve human decision-making in classification tasks, not only by providing fairly accurate predictions, but also in their ability to generate cogent narrative explanations of those predictions. Prior work has demonstrated that people generally find AI narrative explanations to be understandable, trustworthy, and convincing for changing beliefs and opinions; however, less is known about the impact of narrative explanations on objective human decision-making performance. Here we conduct a large-scale human behavioral experiment to evaluate decision-making performance with LLM-generated narrative explanations of varying persuasiveness. We found the degree of persuasiveness, or lack thereof, for LLM-based explanations did not meaningfully impact decision accuracy over a simple AI prediction alone, in agreement with typical results with explainable AI based on feature importance. We found evidence that narratives increased reliance on AI, but both when the AI prediction was correct and incorrect. Exploratory analyses also indicated that the more persuasive narratives may have had a detrimental effect on decision response times and the ability to discriminate between a correct and incorrect AI prediction. Overall, this work indicates that including narrative explanations with AI predictions may involve tradeoffs for decision-making performance, and more work is needed to determine how and when narrative explanations impact human decision-making.