This paper analyzes the successful communication probability between two intermittently-powered nodes in a homogeneous energy harvesting (EH) mesh network. Powering devices using EH can enable networks to operate indefinitely; however, with limited energy storage and in scarce EH conditions, nodes may only be intermittently-powered. This reduces the effectiveness of conventional networking techniques, where listening modes of radios deplete the storage too quickly, rendering nodes useless. This is particularly problematic in the deployment of mesh networks, where there is no provision of a high-power coordinator. To counter this, wake-up receivers (WuRxs) provide extended listening time without the need for a high power conventional radio, but with a cost to sensitivity. Therefore, listening time must be balanced with transmission and wake-to-receive cost, where if all the harvested energy is spent listening none remains to transmit, and vice versa. From stochastic analysis and simulation of the energy usage in mesh nodes, we obtain the optimum transmission load to maximize goodput, which is the rate of successful communications. We include the cost of each wake-up based on the network size in our goodput analysis. Simulations for a fixed number of homogeneous nodes verify this. Furthermore, we model and evaluate the energy consumption trade-off between transmit power and WuRx sensitivity to enable the maximum goodput.