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Can ensemble density functional theory yield accurate double excitations?

The recent use of a new ensemble in density functional theory (DFT) to yield direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments suggest that direct corrections at the exchange level should not be sufficient. We show that in principle, EDFT with direct corrections can yield accurate doubles and explain the error in naive formal arguments about TDDFT. Exact calculations and analytic results on a simple model, the Hubbard dimer, illustrate the results, showing that the answer to the title question is typically yes.