In the evolving domain of Human Activity Recognition (HAR) using Internet of Things (IoT) devices, there is an emerging interest in employing Deep Generative Models (DGMs) to address data scarcity, enhance data quality, and improve classification metrics scores. Among these types of models, Generative Adversarial Networks (GANs) have arisen as a powerful tool for generating synthetic data that mimic real-world scenarios with high fidelity. However, Human Gesture Recognition (HGR), a subset of HAR, particularly in healthcare applications, using time series data such as allergic gestures, remains highly unexplored. In this paper, we examine and evaluate the performance of two GANs in the generation of synthetic gesture motion data that compose a part of an open-source benchmark dataset. The data is related to the disease identification domain and healthcare, specifically to allergic rhinitis. We also focus on these AI models' performance in terms of fidelity, diversity, and privacy. Furthermore, we examine the scenario if the synthetic data can substitute real data, in training scenarios and how well models trained on synthetic data can be generalized for the allergic rhinitis gestures. In our work, these gestures are related to 6-axes accelerometer and gyroscope data, serving as multi-variate time series instances, and retrieved from smart wearable devices. To the best of our knowledge, this study is the first to explore the feasibility of synthesizing motion gestures for allergic rhinitis from wearable IoT device data using Generative Adversarial Networks (GANs) and testing their impact on the generalization of gesture recognition systems. It is worth noting that, even if our method has been applied to a specific category of gestures, it is designed to be generalized and can be deployed also to other motion data in the HGR domain.