The phonon dispersion of ice VII and that of its proton-ordered analog ice VIII are investigated through a combination of inelastic x-ray scattering (IXS) measurements and first-principles calculations of the oxygen sublattice dynamic structure factor. Particular attention is devoted to hydrogen-disorder in ice VII, addressed theoretically through a statistical ensemble of fictitious ordered supercell configurations. Similar phonon densities of states are found in both phases but are significantly less structured in the case of ice VII. Our data further show that, despite a full proton disorder, the acoustic phonon branches in this phase clearly inherit the periodicity of its body-centered cubic oxygen lattice. The calculations predict, however, the presence of gap openings in the one-atom phonon dispersion. These predictions are supported by revisiting the analysis of previous single-crystal IXS measurements along the longitudinal [111] branch of ice VII.