With the recent advances in autonomous underwater vehicle (AUV) technology, it has become feasible to deploy AUV fleets as ad hoc networks for coordinated missions such as remote intelligence, area mapping, and tactical surveillance. In these unattended missions, AUVs are typically sent by a central node, such as a submarine, and they move autonomously. Although there is no need for continuous monitoring of AUV nodes, the central node may occasionally need to broadcast a message to all nodes in the fleet to announce any mission change, such as re-routing or ordering them to return back to the base. However, maximum duration of the mission depends on the lifetime of the AUV network, which is limited by the size and capacity of on-board batteries. This necessitates the detailed analysis of energy consumption characteristics and lifetime constraints in order to avoid operational failure. Here we study the connectivity properties of an energy-constrained ad-hoc AUV network through broadcast simulations. We obtained results with respect to the number of packets transmitted, the total number of nodes, and their mobility characteristics. Our results provide key parameters that must be taken into account in the design and deployment of AUV networks.