Is it possible to rapidly bring a cell back to equilibrium after charging/discharging by applying a current flow in the opposite direction?
The diagram you show is a simplified model of a cell. That can circuit can be brought back quickly to equilibrium as you describe.
However, a real cell is much more complicated, and has many higher order effects. If the Cp and its associated resistors are a correction to the 'zeroth order' behaviour of an ideal cell, then a real cell has many more corrections to the corrections. Unfortunately, they tend to be temperature sensitive, and long-term history dependent, so can't really be used for accurate prediction of useful things like state of charge in the middle ranges of SOC.