As large-scale dense and often randomly deployed wireless sensor networks (WSNs) become widespread, local information exchange between co-located sets of nodes may play a significant role in handling the excessive traffic volume. Moreover, to account for the limited life-span of the wireless devices, harvesting the energy of the network transmissions provides significant benefits to the lifetime of such networks. In this paper, we study the performance of communication in dense networks with wireless energy harvesting (WEH)-enabled sensor nodes. In particular, we examine two different communication scenarios (direct and cooperative) for data exchange and we provide theoretical expressions for the probability of successful communication. Then, considering the importance of lifetime in WSNs, we employ state-of-the-art WEH techniques and realistic energy converters, quantifying the potential energy gains that can be achieved in the network. Our analytical derivations, which are validated by extensive Monte-Carlo simulations, highlight the importance of WEH in dense networks and identify the trade-offs between the direct and cooperative communication scenarios.