Load profile synthesis is a commonly used technique for preserving smart meter data privacy. Recent efforts have successfully integrated advanced generative models, such as the Generative Adversarial Networks (GAN), to synthesize high- quality load profiles. Such methods are becoming increasingly popular for conducting privacy-preserving load data analytics. It is commonly believed that performing analyses on synthetic data can ensure certain privacy. In this paper, we examine this common belief. Specifically, we reveal the privacy leakage issue in load profile synthesis enabled by GAN. We first point out that the synthesis process cannot provide any provable privacy guarantee, highlighting that directly conducting load data analytics based on such data is extremely dangerous. The sample re-appearance risk is then presented under different volumes of training data, which indicates that the original load data could be directly leaked by GAN without any intentional effort from adversaries. Furthermore, we discuss potential approaches that might address this privacy leakage issue.