The tasks of out-of-domain (OOD) intent discovery and generalized intent discovery (GID) aim to extend a closed intent classifier to open-world intent sets, which is crucial to task-oriented dialogue (TOD) systems. Previous methods address them by fine-tuning discriminative models. Recently, although some studies have been exploring the application of large language models (LLMs) represented by ChatGPT to various downstream tasks, it is still unclear for the ability of ChatGPT to discover and incrementally extent OOD intents. In this paper, we comprehensively evaluate ChatGPT on OOD intent discovery and GID, and then outline the strengths and weaknesses of ChatGPT. Overall, ChatGPT exhibits consistent advantages under zero-shot settings, but is still at a disadvantage compared to fine-tuned models. More deeply, through a series of analytical experiments, we summarize and discuss the challenges faced by LLMs including clustering, domain-specific understanding, and cross-domain in-context learning scenarios. Finally, we provide empirical guidance for future directions to address these challenges.