In a heterogeneous cellular network (HetNet) consisting of multiple different types (tiers) of base stations (BSs), the void cell event in which a BS does not have any users has been shown to exist due to user-centric BS association and its probability is dominated by the cell load of each tier. Such a void cell phenomenon has not been well characterized in the modeling and analytical framework of simultaneous wireless information and power transmission (SWIPT) in a HetNet. This paper aims to accurately exploit the fundamental performance limits of the SWIPT between a BS and its user by modeling the cell-load impact on the downlink and uplink transmissions of each BS. We first characterize the power-splitting receiver architecture at a user and analyze the statistical properties and limits of its harvested power and energy, which reveals how much of the average energy can be harvested by users and how likely the self-powered sustainability of users can be achieved. We then derive the downlink and uplink rates that characterize the cell-load and user association effects and use them to define the energy efficiency of a user. The optimality of the energy efficiency is investigated, which maximizes the SWIPT performance of the receiver architecture for different user association and network deployment scenarios.