In a Fog-Radio Access Network (F-RAN), edge caching and fronthaul connectivity to a cloud processor are utilized for the purpose of content delivery. Additional Device-to-Device (D2D) communication capabilities can support the operation of an F-RAN by alleviating fronthaul and cloud processing load, and reducing the delivery time. In this work, basic limits on the normalized delivery time (NDT) metric, which captures the high signal-to-noise ratio worst-case latency for delivering any requested content to the users, are derived. Assuming proactive offline caching, out-of-band D2D communication, and an F-RAN with two edge nodes and two users, an information-theoretically optimal caching and delivery strategy is presented. Unlike prior work, the NDT performance is studied under pipelined transmission, whereby the edge nodes transmit on the wireless channel while simultaneously receiving messages over the fronthaul links, and the users transmit messages over the D2D links while at the same time receiving on the wireless channel. Insights are provided on the regimes in which D2D communication is beneficial, and the maximum improvement to the latency is characterized.