Einstein showed that energy is matter; for something to exist in a physical sense it must be incarnated as matter. So on the face of it - it seems that the answer should be no.
However what about empty space - it certainly exists. Then there is no matter and hence no energy, and since also there is no matter space cannot be curved so energy can't be stored in the curvature of space.
It’s perhaps worth pointing out that Einstein’s equation with the Cosmological constant shows that empty space has an associated energy.