The spread of machine learning models, coupled with by the growing adoption of electronic health records (EHRs), has opened the door for developing clinical decision support systems. However, despite the great promise of machine learning for healthcare in low-middle-income countries (LMICs), many data-specific limitations, such as the small size and irregular sampling, hinder the progress in such applications. Recently, deep generative models have been proposed to generate realistic-looking synthetic data, including EHRs, by learning the underlying data distribution without compromising patient privacy. In this study, we first use a deep generative model to generate synthetic data based on a small dataset (364 patients) from a LMIC setting. Next, we use synthetic data to build models that predict the onset of hospital-acquired infections based on minimal information collected at patient ICU admission. The performance of the diagnostic model trained on the synthetic data outperformed models trained on the original and oversampled data using techniques such as SMOTE. We also experiment with varying the size of the synthetic data and observe the impact on the performance and interpretability of the models. Our results show the promise of using deep generative models in enabling healthcare data owners to develop and validate models that serve their needs and applications, despite limitations in dataset size.