Multi-channel medium access control (MMAC) has the potential to significantly improve the network throughput by enabling parallel transmissions over different frequency channels. In many MMAC protocols, nodes exchange control packets over a dedicated control channel (CC). The CC transmission rate (CCR) is usually set to the lowest possible value, so as to maximize the reachability of control packets. However, in a multi-hop ad hoc network, this choice of the CCR may lead to a CC bottleneck, especially under high traffic load. While increasing the CCR can alleviate this bottleneck and improve the single-hop MMAC performance, it may also increase the number of hops along the path and hence degrade the endto- end network performance. In this paper, we investigate the impact of the CCR on the performance of a multi-channel, multi-hop wireless network under a general MMAC protocol. To derive the queuing and channel access delays, we model the network as a G/G/1 queuing system. In our analysis, we consider detailed packet-level operations and non-saturated traffic. The average number of hops is also analytically obtained when nodes are randomly distributed. Our analysis is evaluated via network simulations, using 802.11a parameters. The simulation and numerical results reveal that the lowest transmission rate is not the optimal CCR. Our simulations show that the received power threshold has a significant impact on the optimal CCR.