Consider an intermittently-connected mobile network consisting of n relay nodes, a single source node, and m destination nodes exhibiting a stochastic model for mobility. Each mobile relay node is also equipped with finite storage. We seek to analyze the performance of Multicast enabled by Network Coding in such a network under the store, carry, and forward paradigm, and compare its performance to a simple custodial-multicast scheme. Though accurate analysis of network-coded multicast is very complicated, we derive a provable way to obtain tight bounds on the performance. We then develop a queuing-theoretic framework to analyze the steady-state throughput performance of the network-coded scheme under this setup, which is then solved iteratively. The framework developed thus enables speedy evaluation of the communication protocols described. Our analytical results, supported by simulation studies, show that the networkcoding- based scheme offers considerable improvement for the case when the storage size of the relay nodes is small and when the number of destination nodes is large.