We examine the implications of electrostatic interactions on formation of polyelectrolyte multilayers, in application to field-effect based biosensors for label-free detection of charged macromolecules. We present a quantitative model to describe the experimental potentiometric observations and discuss its possibilities and limitations for detection of polyelectrolyte adsorption. We examine the influence of the ionic strength and pH on the sensor response upon polyelectrolyte layer-by-layer formation. The magnitude of potential oscillations on the sensor-electrolyte interface predicted upon repetitive adsorption charge-alternating polymers agrees satisfactorily with experimental results. The model accounts for different screening by mobile ions in electrolyte and inside tightly interdigitated multilayered structure. In particular, we show that sensors' potential oscillations are larger and more persistent at lower salt conditions, while they decay faster with the number of layers at higher salt conditions, in agreement with experiments. The effects of polyelectrolyte layer thickness, substrate potential, and charge regulation on the sensor surface triggered by layer-by-layer deposition are also analyzed.