In this paper, we investigate the secrecy energy-efficiency (SEE) of a multi-user downlink non-orthogonal multiple access (NOMA) system assisted by multiple ambient backscatter communications (AmBC) in the presence of a passive eavesdropper. We analyze both the trade-off and the ratio between the achievable secrecy sum-rate and total power consumption. In the special case of two backscatter devices (BDs), we derive closed-form solutions for the optimal reflection coefficients and power allocation by exploiting the structure of the SEE objective and the Pareto boundary of the feasible set. When more than two BDs are present, the problem becomes analytically intractable. To address this, we propose two efficient optimization techniques: (i) an exhaustive grid-based benchmark method, and (ii) a scalable particle swarm optimization algorithm. Furthermore, we design a deep learning-based predictor using a feedforward neural network (FNN), which closely approximates the optimal solutions. Numerical results show that the inclusion of AmBC significantly improves SEE, with gains up to 615% compared to conventional NOMA in high-noise regimes. Additionally, the FNN model achieves more than 95% accuracy compared to the optimal baseline, while reducing complexity. Finally, we employ SHAP (SHapley Additive exPlanations) to interpret the learned model, revealing that the most influential features correspond to the dominant composite channel components, in accordance with the theoretical system model. This demonstrates the potential of explainable artificial intelligence to build trust in energy-efficient and secure AmBC-NOMA systems for next-generation internet of things applications.