Can centrifugal force inside Earth's outer core overcome gravity?

On the surface of the Earth the net force (centrifugal + gravitational) is strongly inwards and is roughly constant. As you descend into the earth, both the centrifugal force and the gravitational force decrease roughly in proportion to r. So gravity will continue to strongly dominate. The situation is a little different near the poles since the two forces there are roughly at right angles. Nevertheless the entire earth is in an isostatic equilibrium that includes these effects. The surfaces of equal (gravitational + centrifugal) potential form concentric slightly oblate spheroids. Convection currents driven by heat in the core are about the only thing that can disturb the equilibrium in the interior. These convection currents will behave differently at different latitudes due to the rotation, so it's likely there are some differences in structure between the equator and the poles.