Energy harvesting is an emerging technology for enabling green, sustainable, and autonomous wireless networks. In this paper, a large-scale wireless network with energy harvesting transmitters is considered, where a group of transmitters forms a cluster to cooperatively serve a desired receiver amid interference and noise. To characterize the link-level performance, closed-form expressions are derived for the transmission success probability at a receiver in terms of key parameters such as node densities, energy harvesting parameters, channel parameters, and cluster size, for a given cluster geometry. The analysis is further extended to characterize a network-level performance metric, capturing the tradeoff between link quality and the fraction of receivers served. Numerical simulations validate the accuracy of the analytical model. Several useful insights are provided. For example, while more cooperation helps improve the link-level performance, the network-level performance might degrade with the cluster size. Numerical results show that a small cluster size (typically 3 or smaller) optimizes the network-level performance. Furthermore, substantial performance can be extracted with a relatively small energy buffer. Moreover, the utility of having a large energy buffer increases with the energy harvesting rate as well as with the cluster size in sufficiently dense networks.