Scarcity of user data continues to be a problem in research on conversational user interfaces and often hinders or slows down technical innovation. In the past, different ways of synthetically generating data, such as data augmentation techniques have been explored. With the rise of ever improving pre-trained language models, we ask if we can go beyond such methods by simply providing appropriate prompts to these general purpose models to generate data. We explore the feasibility and cost-benefit trade-offs of using non fine-tuned synthetic data to train classification algorithms for conversational agents. We compare this synthetically generated data with real user data and evaluate the performance of classifiers trained on different combinations of synthetic and real data. We come to the conclusion that, although classifiers trained on such synthetic data perform much better than random baselines, they do not compare to the performance of classifiers trained on even very small amounts of real user data, largely because such data is lacking much of the variability found in user generated data. Nevertheless, we show that in situations where very little data and resources are available, classifiers trained on such synthetically generated data might be preferable to the collection and annotation of naturalistic data.