Advanced wireless applications such as sensor networks involve a close interaction between the communication and computation processes that deliver the services under stringent power constraints. Wireless network distributed computing (WNDC) is a potential solution to reducing the power consumption per node as well as that of the network. In WNDC, a computational task is executed among a network of collaborative nodes in a distributed manner as against performing the same task on a single node. In addition to providing power savings, WNDC enables power demand-supply matching that allows for system operation under a constrained power supply such as solar power. This paper presents fundamental power efficiency analysis of WNDC. The conditions for achieving power demand-supply matching and positive network power savings under power and computational latency constraints are derived. The results show the impact of non-linearity in the computational system characteristics and the communication overhead on the power savings.