A notable problem in Brain-Computer Interface (BCI) is the burden of collecting an adequate amount of training data to be used in estimating a robust classifier model. This study explores the prospect of using Generative Adversarial Networks (GANs), a novel family of generative models, to perform data augmentation for generating artificial training data that are used in the classification of P300 event-related potentials in electroencephalogram (EEG) signals. In this regard, we consider two popular GANs, namely, Deep Convolutional Generative Adversarial Networks (DCGAN) and Wasserstein GAN with Gradient Penalty (WGAN-GP), and explore their efficacy in generating artificial EEG data in both subject-specific and subject-independent contexts. The results show that data augmentation using both DCGAN and WGAN-GP could lead to improved classification performance. However, the operating conditions that an improvement is observed differ between the subject-specific and subject-independent classification schemes. In particular, we observe that a transition from a relatively small to large training sample size per subject would generally lead to a better classification performance in training subject-specific classifiers; however, when a limited number of subjects is available, this transition could potentially result in an opposite effect in case of subject-independent classification.