Can the mass of an object be considered as concentrated at its center of mass for purposes of computing its rotational inertia? If yes, explain why. If no, offer a counterexample.

No, the mass of an object cannot be considered as concentrated at its center of mass for purposes of computing its rotational inertia. Consider a situation in which the point of center of gravity of the object does not coincide with its center of mass, then the object would rotate around its center of gravity and the rotational inertia would correspond to that axis of rotation.
If one assumes that the center of gravity is at the same point as center of mass, then one will come in contradiction with the experimental results because according to the person, the object rotational inertia is calculated about the axis passing through the center of mass (coinciding with center of gravity), however, in reality that is not the case.