Reservation-based wireless TDMA networks can provide deterministic quality-of-service guarantees to multi-hop data flows. The challenge is to route the flows and schedule appropriate transmission slots in a resource-efficient way. In this paper, we study the fundamental question whether multi-path routing, i.e. concurrent use of multiple paths for transmission of data belonging to the same flow, may yield better solutions to the joint routing and slot scheduling problem than single-path routing approaches. To answer this question, we first define an accurate network model. We then devise a branch-and-bound algorithm that computes optimal multi-path and single-path solutions to the joint routing and slot scheduling problem. We apply the algorithm to a large number of scenarios in randomly generated networks and compare optimal network load and end-to-end delay metric values in order to quantify the benefit of multi-path routing over the single-path approach. Our results show that in the studied settings, it is quite rare for multi-path solutions to surpass the optimal single-path solution. Multi-path routing should therefore not be considered an option to improve performance in reservation-based TDMA networks with random topologies.