Sustained periods of southward interplanetary magnetic field can result in strong magnetospheric convection, during which, the Alfven layer, separating regions of sunward convection and closed drift paths, migrates earthwards. Plasmasheet electrons then have direct access to the inner magnetosphere, traversing the dawn sector before crossing the magnetopause, and present a potential seed population for the radiation belts. Here we examine, for the first time, whether energetic electrons can be sufficiently energised during their drift, via resonant interactions with whistler-mode chorus waves, so as to pass the Alfven layer prior to leaving the system. We utilise a natural coordinate system for magnetosphere convection, (U,B,K) space, in which we calculate the drift trajectories, electron energies on open drift paths, and drift times. The acceleration time from resonant chorus-wave particle interactions is calculated using the Versatile Electron Radiation Belt model (VERB) first as a 2-D diffusion equation and then in 4-D convection-diffusion mode. Comparing the drift times to the acceleration timescales we find that interactions with chorus waves do result in a portion of the electrons on open drift paths passing the Alfven energy. However, whether this acceleration occurs sufficiently quickly depends on the energy distribution of the electron population.