To first order, the screening effect of grid 2 (held at a constant voltage with respect to the cathode) makes the electric field at the cathode almost independent of the plate-cathode voltage (extremely high mu, hence the large plate resistance). In normal pentode operation, the screen bypass capacitor helps maintain the screen-cathode voltage even as the screen current changes with plate voltage. Note that changing the screen voltage on purpose does change the cathode current: there is a “screen mu” parameter that describes the triode behavior of the cathode-grid1-grid2 portion of the pentode. This parameter is generally low (e.g. 4.5 for a 6146 power tube). Therefore, if the screen is powered through a resistor, with no bypass capacitor, the stage gain is reduced: see any tube textbook for details.