Covert communication is achieved if the transmitter (Alice) sends messages to a legitimate receiver (Bob) without detection by an attentive warden (Willie). Recently, there has been significant work on establishing the limits of such covert communication, including our work demonstrating that a cooperative jammer can greatly improve the throughput of covert communication systems. However, this previous work has considered a discrete-time model, with the implicit implication that the results will be similar on the true continuous-time model of the physical channel. In this paper, we consider covert communication over the continuous-time channel model to understand the throughput scaling for large blocklengths. For the Alice-Bob-Willie scenario, the results from the discrete-time channel generally follow. However, when a jammer is added to the environment, we demonstrate that timing offsets between Alice's signal and that of the jammer allow for the application of co-channel interference mitigation techniques at Willie's detector, which call into question whether our previous results suggesting an improvement in the covert throughput with the help of the jammer will be obtained in practice. Finally, we consider initial approaches to thwart such a detector and achieve improved throughput scaling in the presence of the jammer.