Cooperative Non-Orthogonal Multiple Access (CNOMA) offers a promising approach to optimize wireless network performance by combining Non-Orthogonal Multiple Access (NOMA) principles with cooperative diversity for beyond 5G (B5G) and 6G systems. This paper investigates the connectivity of cell-edge users in CNOMA frameworks where the main (BS to cell-edge user) and cooperative (relay user to cell-edge user) links are modeled as correlated Rayleigh fading channels. The primary contribution is studying the effect of channel correlation and deriving a closed-form expression for the connectivity probability. We analyze the correlation effect between channels by leveraging the novel approach called Copula theory, specifically the Farlie-Gumbel-Morgenstern (FGM) Copula. Furthermore, we extend the derived connectivity probability to encompass the connectivity of the cell-edge user in conventional non-cooperative NOMA and Orthogonal Multiple Access (OMA) scenarios. The obtained expressions are validated via Monte-Carlo simulations. Additionally, this paper evaluates the impact of channel correlation across various scenarios, including the low and high Signal-to-Noise Ratio (SNR) regimes, as well as under positive dependence, independence, and negative dependence structures.