The multiple nodes forming a Radio Frequency (RF) Energy Harvesting Network (RF-EHN) have the capability of converting received electromagnetic RF signals in energy that can be used to power a network device (the energy harvester). Traditionally the RF signals are provided by high power transmitters (e.g., base stations) operating in the neighborhood of the harvesters. Admitting that the transmitters are spatially distributed according to a spatial Poisson process, we start by characterizing the distribution of the RF power received by an energy harvester node. Considering Gamma shadowing and Rayleigh fading, we show that the received RF power can be approximated by the sum of multiple Gamma distributions with different scale and shape parameters. Using the distribution of the received RF power, we derive the probability of a node having enough energy to transmit a packet after a given amount of charging time. The RF power distribution and the probability of a harvester having enough energy to transmit a packet are validated through simulation. The numerical results obtained with the proposed analysis are close to the ones obtained through simulation, which confirms the accuracy of the proposed analysis.