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Ambient radio frequency (RF) energy harvesting is widely promoted as an enabler for wireless-power Internet of Things (IoT) networks. This paper jointly characterizes energy harvesting and packet transmissions in grant-free opportunistic uplink IoT networks energized via harvesting downlink energy. To do that, a joint queuing theory and stochastic geometry model is utilized to develop a spatio-temporal analytical model. Particularly, the harvested energy and packet transmission success probability are characterized using tools from stochastic geometry. {Moreover, each device is modeled using a two-dimensional discrete-time Markov chain (DTMC). Such two dimensions are utilized to jointly track the scavenged/depleted energy to/from the batteries along with the arrival/departure of packets to/from devices buffers over time. Consequently, the adopted queuing model represents the devices as spatially interacting queues. To that end, the network performance is assessed in light of the packet throughput, the average delay, and the average buffer size. The effect of base stations (BSs) densification is discussed and several design insights are provided. The results show that the parameters for uplink power control and opportunistic channel access should be jointly optimized to maximize average network packet throughput, and hence, minimize delay.