What would be the potential effects of not having an accumulator in the hydraulic system?
Accumulators act as storage for flow. At times of peak flow demand, the accumulator delivers a large flow supply at nominal pressure until its oil has been used up, after which the maximum flow is the pump flow. The same functionality that a capacitor or a battery has in an electric system.

If there are no accumulators installed:


Peak hydraulic power is greatly reduced: peak flow supply equals the pump flow, and pressure drops when the pump supplies high flow.
Pressure surges are high when the pump is running and demand suddenly stops, the accumulator evens out the pressure peak, again like how a capacitor functions. (From @Gerry comment).