With the rapid expansion of Internet of Everything (IoE) devices and the increasing demand for high-speed data and reliable communication services, particularly within 6G cellular networks (CNs), the design of efficient and robust CNs has become a critical research area. Consequently, enabling massive connections, optimizing network resource utilization, and achieving cost-effective network operation pose significant challenges. To this end, integrated space-ground cellular networks based on control- and user-plane separation (ISGCN-CUPS) architecture has been proposed as a promising solution. Furthermore, it becomes an integral aspect of the broader paradigm of integrated space-air-ground CNs (ISAGCNs). However, scalability poses an issue when increasing the number of connected cellular users, especially when conventional orthogonal multiple access (OMA) is utilized. To address this challenge, this paper introduces the non-orthogonal multiple access (NOMA)-enabled ISGCN-CUPS architecture. Subsequently, we provide an analytical model to analyze the scenarios of proposed architecture. Utilizing stochastic geometry, we derive closed-forms for coverage probabilities over control and data channels, by considering the propagation channel models for control and data channels, both with and without interference. Furthermore, total area spectral and energy efficiencies are computed. The proposed architecture demonstrates significant enhancements in terms of the key evaluation metrics compared to conventional and OMA-enabled ISGCN-CUPS architectures.