We test precision of the Cosmological Paczynski-Wiita (CPW) potential eflecting properties of the Schwarzschild-de Sitter (SdS) spacetimes in modeling dynamical phenomena related to galaxy motion. We consider a simplified model of Magellanic Clouds moving in the field of Milky Way as test particles. Time evolution of their position along trajectories obtained in the CPW framework using the notion of Newtonian time is compared to the one obtained in the fully general relativistic (GR) approach when the time evolution is expressed in terms of time related to the location of Earth in the Galaxy field. The differences in the position-evolution of the Magellanic Clouds obtained in the CPW and GR approaches are given for appropriately chosen values of the Milky Way mass. It is shown that the integrated relativistic corrections represent ~10^-5 part of the Newtonian CPW predictions for the orbital characteristics of the motion and slightly grow with Galaxy mass growing, being at least by one