Energy harvesting is an emerging technology that enhances the lifetime of Internet-of-Things (IoT) applications. Satisfying real-time requirements for these systems is challenging. Dedicated real-time schedulers integrating both timing and energy constraints are required, such as the ED-H scheduling algorithm[1]. However, this algorithm has been proved to be optimal for independent tasks only (i.e., without considering any shared resources), thus preventing its confident deployment into computing infrastructures in which tasks are mostly interdependent. In this paper, we first derive worst-case blocking times and worst-case blocking energy for tasks sharing resources managed by the DPCP protocol[2] and scheduled under the ED-H scheme. Then, we provide a sufficient schedulability test for ED-H-DPCP guaranteeing off-line that both timing and energy constraints will be satisfied, even in the presence of shared resources.