Not when quantum mechanics is taken into account, no. As Simon Bridge said, quantum effects mean that no object can ever have exactly zero thermal energy. However, for many purposes the quantum effects can be ignored; that's why you will often find sources saying (incorrectly, strictly speaking) that objects at absolute zero have zero thermal energy (instead of saying that they have the minimum possible thermal energy allowed by their quantum states).
Also, as Simon said, there is no way to cool an object down to exactly absolute zero; so if we consider the properties of an object at exactly absolute zero, we are considered an idealized limiting case that can never be realized in practice. (That doesn't mean it's not a useful idealization; for many purposes it simplifies things greatly to assume an idealized object with zero temperature.)
There is also another key thing to bear in mind: when we say that an object at absolute zero has "zero energy" (subject to the corrections related to quantum mechanics, as above), we mean zero thermal energy (note that both Simon and I were careful to include that qualifier). The object can still have other kinds of energy that are not thermal: for example, the energy contained in its mass.
The object would still be able to provide an opposing force, because the energy involved doesn't come from the object; it comes from the work being done by striking it. For example, if you hit the object with a hammer, the hammer has kinetic energy, and that kinetic energy can do work against the repulsive force between the atoms in the hammer and the atoms in the object, even if the object itself has zero thermal energy.
