This paper articulates an innovative systems dynamics model of learning based on a predictive cognitive architecture by interrelating six modules: knowledge, affect, cognition, performance, external agents, and context. To test aspects of this model, this paper focuses on cognitive load theory predicting that a manipulation of the learning task can affect at least one of the three types of load (intrinsic, germane and extraneous). More precisely, agency is hypothesized to affect either the intrinsic or extraneous load. Therefore, the goal of this paper is to explore the effect of agency on cognitive load. Thirty-six dyads (1 player and 1 watcher) played a serious game for learning physics for 120 min while dual-EEG was recorded for all participants. Results of time series analysis show that agency (being a player or a watcher) as no effect on the overall cognitive load when the comparison is made either by group (all players versus all watchers), or within a single dyad. Moreover, nor did agency affect instantaneous cognitive load for a vast majority of dyads. Indeed, only four dyads exhibited one or two significant cross-correlations. However, those exceptional cases cannot be generalized. Finer-grained analyses are proposed in the discussion to better explore the role of agency on cognitive load in further research.