For platooning applications, vehicles in a platoon require timely and reliable delivery of road-safety information in order to maintain the stable operation of the platoon. Intra-platoon message broadcast delay (InPB-delay) is a critical metric that is used to measure the message delivery performance in a platoon of vehicles, where a V2V multi-hop broadcast mode is used for message delivery. In this paper, we study the modeling and analyses of the InPB-delay for a platoon of connected and automated vehicles (CAVs), which employs an IEEE 802.11p EDCA mechanism for channel access. A 2-D Markov chain model is first built to describe a backoff procedure of a platoon broadcasting node, which takes into account the four access categories of different priorities in the EDCA mechanism. Based on the Markov model, a theoretical performance model is further derived to investigate the impacts of major system parameters on the InPB-delay, taking into account the effects of both platoon vehicles and non-platoon vehicles. The derived performance model is validated through simulation results and the impacts of major system parameters are investigated through numerical results. The InPB-delay model can be used to provide reference values for system parameter settings in order to ensure the stable operation of a platoon.