Context: Understanding how protostars accrete their mass is a central question of star formation. One aspect of this is to try and understand if the time evolution of accretion rates in deeply embedded objects is best characterised by a smooth decline from early to late stages, or by intermittent bursts of high accretion. Aims: We create synthetic observations of deeply embedded protostars in a large numerical simulation of a molecular cloud, which are compared directly to real observations. The goal is to compare episodic accretion events in the simulation to observations, and to test the methodology used for analysing the observations. Methods: Simple freeze-out and sublimation chemistry is added to the simulation, and synthetic C18O line cubes are created for a large number of simulated protostars. The spatial extent of C18O is measured for the simulated protostars, and compared directly to a sample of 16 deeply embedded protostars observed with the Submillimeter Array. If CO is distributed over a larger area than predicted based on the protostellar luminosity, it may indicate that the luminosity has been higher in the past, and that CO is still in the process of refreezing. Results: Approximately 1% of the protostars in the simulation show extended C18O emission, as opposed to approximately 50% in the observations, indicating that the magnitude and frequency of episodic accretion events in the simulation is too low relative to observations. The protostellar accretion rates in the simulation are primarily modulated by infall from the larger scales of the molecular cloud, and do not include any disk physics. The discrepancy between simulation and observations is taken as support for the necessity of disks, even in deeply embedded objects, to produce episodic accretion events of sufficient frequency and amplitude.