This paper develops an upper bound on the end-to-end transmission capacity of multi-hop wireless networks, in which all nodes are randomly distributed. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form bound on the outage probability is derived in terms of the number of potential paths. This in turn gives an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows us to immediately observe how the number of hops and other network traits affect spatial throughput. Our analysis indicates that predetermined routing approach (such as nearest-neighbor) cannot achieve optimal throughput: more hops are not necessarily helpful in interference-limited networks compared with single-hop direct transmission.