Deep neural networks have recently shown great success in the task of blind source separation, both under monaural and binaural settings. Although these methods were shown to produce high-quality separations, they were mainly applied under offline settings, in which the model has access to the full input signal while separating the signal. In this study, we convert a non-causal state-of-the-art separation model into a causal and real-time model and evaluate its performance under both online and offline settings. We compare the performance of the proposed model to several baseline methods under anechoic, noisy, and noisy-reverberant recording conditions while exploring both monaural and binaural inputs and outputs. Our findings shed light on the relative difference between causal and non-causal models when performing separation. Our stateful implementation for online separation leads to a minor drop in performance compared to the offline model; 0.8dB for monaural inputs and 0.3dB for binaural inputs while reaching a real-time factor of 0.65. Samples can be found under the following link: https://kwanum.github.io/sagrnnc-stream-results/.