In a Fog Radio Access Network (F-RAN), content delivery is carried out using both edge caching and cloud processing. A key design question for F-RANs hence concerns the optimal use of edge and cloud resources. In this work, this problem is addressed from an information theoretic viewpoint by investigating the fundamental limits of the normalized delivery time (NDT) metric, which captures the high signal-to-noise ratio (SNR) worst-case latency for delivering any requested content to the users. Specifically, unlike prior work, the NDT performance of an F-RAN is studied under pipelined fronthaul-edge transmission, whereby edge nodes are capable of simultaneously receiving fronthaul messages from the cloud on fronthaul links while transmitting to the mobile users over the wireless edge channel. Lower and upper bounds on the NDT are derived that yield insights into the trade-off between cache storage capacity, fronthaul capacity and delivery latency and on the impact of fronthaul-edge pipelining.