High-quality recordings of radio frequency (RF) emissions from commercial communication hardware in realistic environments are often needed to develop and assess spectrum-sharing technologies and practices, e.g., for training and testing spectrum sensing algorithms and for interference testing. Unfortunately, the time-consuming, expensive nature of such data collections together with data-sharing restrictions pose significant challenges that limit data set availability. Furthermore, developing accurate models of real-world RF emissions from first principles is often very difficult because system parameters and implementation details are at best only partially known, and complex system dynamics are difficult to characterize. Hence, there is a need for flexible, data-driven methods that can leverage existing data sets to synthesize additional similar waveforms. One promising machine-learning approach is unsupervised deep generative modeling with generative adversarial networks (GANs). To date, GANs for RF communication signals have not been studied thoroughly. In this paper, we present the first in-depth investigation of generated signal fidelity for GANs trained with baseband orthogonal frequency-division multiplexing (OFDM) signals, where each subcarrier is digitally modulated with quadrature amplitude modulation (QAM). Building on prior GAN methods, we developed two novel GAN models and evaluated their performance using simulated data sets with known ground truth. Specifically, we investigated model performance with respect to increasing data set complexity over a range of OFDM parameters and conditions, including fading channels. The findings presented here inform the feasibility of use cases and provide a foundation for further investigations into deep generative models for RF communication signals.