Edge Function-as-a-Service is an emerging computing model that dynamically schedules function executions across distributed edge (close to users) locations to reduce latency and improve user experience. Accurate time-series prediction models, which forecast the future number of function invocations, are crucial for energy-efficient function scheduling, enabling proactive resource allocation. In this work, we evaluate the impact of different neural time-series predictors based on Gaussian processes, recurrent neural networks, and transformer architectures in forecasting the number of function invocations. Furthermore, we propose the Energy-Aware Resource Management (EA-RM) scheduling algorithm, based on a mixed-integer problem, designed to minimize overall energy consumption by reducing the number of edge nodes used. We analyze how prediction accuracy influences function scheduling with respect to energy consumption, using real-world data that include different functions and resources. Experimental results show that the transformer-based predictor outperforms the other considered predictors, leading to more precise function scheduling. Moreover, resource allocation performed through the EA-RM algorithm reduces the energy consumption by ~12-45% on average w.r.t. competitors, and is proven to be more robust w.r.t. the accuracy of the prediction model used.