How would the non-interacting electron orbitals from a perfect DFT solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total wavefunction? Would they be less localised as they do not include interaction effects?
Since Hohenberg-Kohn showed that a functional of the wavefunction could be transformed into a functional of the density, any 'measurements' on the total density would have to yield the same results as measurements on the total wavefunction, I think.
Intuitively, if we imagine a 3-electron system, the ground state consists of spin-up and -down electrons in the lowest state, and a singlet electron in the next state. Since there is correlation and exchange, the total wavefunction would be a superposition of the various possible combinations of these.