This work investigates covert communication in a rate-splitting multiple access (RSMA)-based multi-user multiple-input single-output system, where the random locations of the wardens follow a homogeneous Poisson point process. To demonstrate practical deployment scenarios, imperfect channel state information at the transmitter is considered. Closed-form expressions for the statistics of the received signal-to-interference-plus-noise ratio, along with the analytical formulations for the covertness constraint, outage probability, and effective covert throughput (ECT), are derived. Subsequently, an ECT maximization problem is formulated under covertness and power allocation constraints. This optimization problem is addressed using an alternating optimization-assisted genetic algorithm (AO-GA). Simulation results corroborate the theoretical analysis and demonstrate the superiority of RSMA over conventional multiple access schemes, as well as the effectiveness of the proposed AO-GA.