Quantum plasmonics experiments have on multiple occasions resulted in the observation of quantum coherence of discrete plasmons, which exhibit remarkable preservation of quantum interference visibility, a seemingly surprising feature for systems mixing light and matter with high Ohmic losses during propagation. However, most experiments to date used essentially weakly confined plasmons, which experience limited light-matter hybridization, thus limiting the potential for decoherence. In this paper, we investigate experimentally the robustness of coherence preservation in a plasmonic system: our setup is based on a hole-array chip supporting plasmons near the surface plasma frequency, where plasmonic dispersion and confinement are much stronger than in previous experiments, making the plasmons much more susceptible for decoherence processes. We, however, report preservation of quantum coherence even in these extreme conditions. We generate polarization-entangled pairs of photons using type-I spontaneous parametric down-conversion and transmit one of the photons through a plasmonic hole array that is numerically designed to convert incident single photons into highly dispersive single surface-plasmon polaritons. Our results show that the quality of photon entanglement after the plasmonic channel is unperturbed by the introduction of a highly dispersive plasmonic element. Our findings provide a lower bound of 100 fs for the pure dephasing time for dispersive plasmons in gold, and show that even in a highly dispersive regime surface plasmons preserve quantum mechanical correlations, making possible harnessing of the power of extreme light confinement for integrated quantum photonics.