In this paper, we consider simultaneous information and energy transfer (SWIPT) in unmanned aerial vehicle (UAV)-assisted cellular Internet of Things (IoT) networks, in which the user equipment (UE) locations are modeled as Thomas cluster processes. A realistic air-to-ground communication model is incorporated into the analysis. In particular, different line of sight (LOS) and non-LOS (NLOS) path loss models are considered for the links from the UAVs to UEs and ground base stations (GBSs) to UEs. Three dimensional (3D) antenna patterns are adopted, e.g., a doughnut-shaped antenna radiation pattern is considered for UAVs and a combination of horizontal and vertical antenna pattern is utilized for GBSs. In addition, we employ the power splitting technique in the SWIPT scenario, which allows the UEs to harvest energy and decode information simultaneously using the same received signal. Association probability and energy coverage probability of the UAVs and GBSs are determined. Moreover, an analysis of the successful transmission probability which jointly addresses the energy and signal-to-interference-plus-noise ratio (SINR) coverages is provided. Finally, performance is further investigated via numerical results.