Reconfigurable antenna (RA) has emerged as a disruptive antenna technology with the potential of significantly improving the capacity of wireless links, by agilely reconfiguring its antenna states. Through jointly optimizing antenna state selection, routing and scheduling, it offers another dimension of opportunity to enhance end-to-end (E2E) throughput in multi-hop wireless networks (MWNs). However, the throughput limit of MWNs with RAs has not been well understood, due to challenges in theoretical modeling and computational intractability caused by a large number of states. In this work, we endeavor to systematically study this problem. We first propose a general antenna state-link conflict graph model to capture the intricate state-link association and corresponding interference relationship in the network. Based on this model, we formulate a max-flow based optimization framework to derive the throughput bound of a given MWN. As this problem is NP-hard, we explore column generation to solve it more efficiently, and propose a heuristic algorithm which can also accelerate the optimal solution. Simulation results show that our proposed algorithms can efficiently approach or compute the optimal throughput, and validate the advantage of antenna reconfigurability in MWNs.