In the past few years, the possibility to transfer power wirelessly has experienced growing interest from the research community. Since the wireless channel is subject to a large number of random phenomena, a crucial aspect is the statistical characterization of the energy that can be harvested by a given device. For this characterization to be reliable, a powerful model of the propagation channel is necessary. The recently proposed Generalized-K model has proven to be very useful, as it encompasses the effects of path-loss, shadowing and fast fading for a broad set of wireless scenarios, and it is analytically tractable. Accordingly, the purpose of this paper is to characterize, from a statistical point of view, the energy harvested by a static device from an unmodulated carrier signal generated by a dedicated source, assuming that the wireless channel obeys the Generalized-K propagation model. Specifically, using simulation-validated analytical methods, this paper provides exact closed-form expressions for the average and variance of the energy harvested over an arbitrary time period. The derived formulation can be used to determine a power transfer plan that allows multiple or even massive numbers of low-power devices to operate continuously, as expected from future network scenarios such as IoT or 5G/6G.