Sure. The zero point energy of any quantum system is the energy remaining in the ground state.
To take an example, a hydrogen atom at absolute zero has no translational motion (obviously) and its one electron will be in the 1s orbital, which is the ground state. But that electron still has energy. So that is a form of zero point energy. It is unextractable energy, because there is no lower state available to the system, but it is still energy.
Similarly, a diatomic molecule has a bond between the two atoms and and this bond can vibrate. But the vibration is quantised, so the vibrational energy of the bond can only be present in certain fixed amounts (this is how the lines in the IR spectrum arise, from transitions between these vibrational energy levels.) In the ground state, there is still some residual vibration present. So at absolute zero, the bond still vibrates a bit. That is zero point energy.
So, when matter is at absolute zero, it is in the ground state in all its degrees of freedom, but there is still energy present in some of these modes. This is zero point energy.
The vacuum is a special case, arising from the QED idea that fields too cannot be said to have definitively zero energy - hence the vacuum itself has a zero point energy, just as matter does.
So in the context you have in mind, to be accurate you should speak of the zero point energy of the vacuum or of the various fields, because you are not talking about the zero point energy of matter.
People get a bit lazy sometimes and forget this distinction, because physicists are all excited about hip and trendy virtual photons and things, but to a chemist, zero point energy is just a humdrum thing: the energy of the ground state of whatever atom or molecule one is talking about.
Thanks for the clarification.