Neural motion planners can increase motion planning quality and, by reducing collision detection computations, improve runtime. However, when profiled on an accelerator-rich hardware system, neural planning contributes to more than 50% of the runtime, and 33% of the computation energy consumption, motivating the design of compute- and energy-efficient neural planners. In this work, we propose a neural planner using Binary Encoded Labels (BEL), where a set of binary classifiers are used instead of a typical regression network. Compared to conventional regression-based neural planners, the proposed BEL neural planner reduces neural planning (inference) computation and collision detection checks while maintaining equal or higher motion planning success rate across various motion planning benchmarks. This computation reduction can improve the computation energy efficiency of neural planning by$1.4 \times-21.4 \times$. Finally, we demonstrate the trade-offs between collision detection and neural planning computation to maximize energy efficiency for different hardware configurations.