What is lacking from the question is a logical framework for the possibility suggested — that carbon dioxide can be a source of energy — and I suspect that this is because it lacks a clear chemical conception of what energy is and how it is formed in living organisms.
The generation of energy in a biological context can be considered as the consequence of a chemical reaction or physico-chemical process which involves a negative (Gibbs) free energy change. For use by the cell (except in exceptional circumstances like heat generateion) the energy released in this process must be used to drive the thermodynamically unfavourable formation of a molecule (e.g. ATP) in which this can be ‘stored’. The stored energy is used when the hydrolysis of ATP is coupled to a thermodynamically unfavourable biological reaction or change, hence providing the ‘energy’ for it. This topic is covered in most biochemical texts, e.g. Berg et al..
So if carbon dioxide were to be a source of energy, it would have to undergo some reaction with a negative (Gibbs)free energy change. Other carbon compounds that are sources of energy are so by virtue of their ability to be oxidized (again see Berg et al.). However, as has already been mentioned in a comment, carbon dioxide is the most oxidized form of carbon and so cannot generate energy this way:
So unless the question could proposes another chemical or physico-chemical in which carbon dioxide could participate that has negative (Gibbs)free energy change, there is no reason to consider the postulate.