This document serves as supplementary material for our journal submission, providing detailed mathematical proofs and derivations that support the results presented in the main manuscript. Specifically, under a modeling framework that jointly considers transceiver hardware impairments and imperfect successive interference cancellation (SIC), we systematically derive and prove from an optimality perspective that: when the residual interference coefficient approaches 1 (i.e., SIC becomes severely ineffective), there exists an optimal solution such that the common stream beamformer satisfies $\bm w_c^\star=\bm 0$, and hence the optimal rate-splitting multiple access (RSMA) transmission structure degenerates into space division multiple access (SDMA). This conclusion provides a verifiable theoretical justification for the convergence phenomenon observed in simulations, namely that "the RSMA performance gradually approaches that of SDMA as SIC degrades", and can also serve as a reference for multiple-access selection and system design in SIC-limited scenarios.