The hot and cold pressures will be the same with or without air cushion or surge damper - the hot side is fed by the cold supply with no valving in between so the pressure will equalise.
Hmmm. then what is the none return valve on the cold water inlet to the heater?
In a pressure switch controlled system the cold water pump delivers water to both cold and hot systems at the same pressure. But the water that enters the heater passes through the NRV on the inlet to the heater. When the taps are closed the pump continues to deliver water that begins to compress the air cap in the hot tank until the pressure switch is satisfied and the pump
As the water in the heater rises in temperature it expands into the air cap raising it's pressure. The pressure does not equalise into the cold system because of NRV.
When a true mixer tap is opened, the raised hot water pressure will overcome the lower pressure cold water and deliver from the hot tank because the ultra compressed air cap provides the flow, untill the pressure has reduced to match the cold supply pressure, at which point the cold will begin to flow due to the resilience of the plastic hoses, as the pressure continues to drop a few moments later the pressure switch detects the drop and starts to pump.
Often with showers the pump can actually deliver mor water than the shower can pass, so as the pump operates it can start to raise the pressure in the pipework and the water heater. As the pressure rises the air cap in the hot tank also compresses. If the pump is strong enough, it can add enough pressure to retrip the pressure switch, which stops the cold flow, but the recompressed air cap in the hot tank can continue to deliver hot water.
This results in repeating pulses of hot and warm water synchronised with the pump pulsing.
To largely overcome this problem, fitting a similar sized air cap to the cold water pipes (a surge or pressure damper) provides the cold water system with a similar pressure resilience as the hot system, and crucially prevents such wide short term water temperature variations and improving comfort and control.