Charge transfer (CT) excitation energies are known to be challenging for standard time-dependent (TD) density functional theory (DFT) calculations. Perturbative ensemble DFT (pEDFT) was suggested as an easy-to-implelemt, low-cost alternative to TDDFT, because it is an in principle exact theory for calculating excitation energies that produces useful valence excitation energies. Here, we examine analytically and numerically (based on the benzene-tetracyanoethylene complex) how well pEDFT performs in the CT limit. We find that pEDFT is qualitatively correct in that it follows the Mulliken limit while being only weakly dependent on the underlying density functional approximation. We observe, however, that quantitatively pEDFT is not as accurate as TDDFT. We attribute this to the emergence of a new type of self-interaction-like term that adversely affects the computation.