An emerging trend of next generation communication systems is to provide network edges with additional capabilities such as storage resources in the form of caches to reduce file delivery latency. To investigate the impact of this technique on latency, we study the delivery time of a cache-aided broadcast-relay wireless network consisting of one central base station, $M$ cache-equipped transceivers and $K$ receivers under finite precision channel state information (CSI). We use the normalized delivery time (NDT) to capture the worst-case per-bit latency in a file delivery. Lower and upper bounds on the NDT are derived to understand the influence of $K,M$, cache capacity and channel quality on the NDT. In particular, regimes of NDT-optimality are identified and discussed.