There is an increasing demand for underwater communication, not least manifested in a need to distribute and retrieve data from networks of underwater sensors.  Whilst there are exceptions, acoustic techniques are generally the only viable means of communication. However, transmitting information acoustically is energy-intensive and can limit the lifetime of battery-powered platforms. Through simulations, this paper statistically investigates a recent transmission power controller, developed for underwater networks of static, battery-powered modems.  The controller is self-configuring, as the modems' locations are assumed to be unknown. Further, the controller is fully distributed for scalability and adaptability reasons. The method involves a $k$-nearest neighbor approach when selecting transmission power for packet forwarding, i.e., the transmission power is selected such that only the $k$ closest modems will receive a packet. A well-known flooding-based routing protocol suitable for ad-hoc networks is employed to assess the energy consumption with and without the power controller. The evaluation is based on simulations using 16 modems placed randomly in a square area with varying sizes and choices of $k$. The results show that in a small and dense network, up to 61-68\% energy can be saved with a minor 7\% drop in packet delivery ratio.