You can very probably do it, but it may not have the desired effect that you think it will. These electric showers vary their temperature of the shower water by varying the volume of cold water passing the heating element inside the shower.
Let me ask, if you turn the temperature down on the shower control, does the flow of water increase to a more acceptable 'power', to use your term? If the answer is yes, installing a pump to the input side won't alter anything. You are being limited by the capacity (in Watts) of the electric system to heat the water from cold to shower-hot.