Hybrid non-orthogonal multiple access (NOMA), which organically combines pure NOMA and conventional OMA, has recently received significant attention to be a promising multiple access framework for future wireless communication networks. However, most of the literatures on hybrid NOMA only consider fixed order of successive interference cancellation (SIC), namely FSIC, for the NOMA transmission phase of hybrid NOMA, resulting in limited performance. Differently, this paper aims to reveal the potential of applying hybrid SIC (HSIC) to improve the energy efficiency of hybrid NOMA. Specifically, a HSIC aided hybrid NOMA scheme is proposed, which can be treated as a simple add-on to the legacy orthogonal multiple access (OMA) based network. The proposed scheme offers some users (termed ``opportunistic users'') to have more chances to transmit by transparently sharing legacy users' time slots. For a fair comparison, a power reducing coefficient $β$ is introduced to ensure that the energy consumption of the proposed scheme is less than conventional OMA. Given $β$, the probability for the event that the achievable rate of the proposed HSIC aided hybrid NOMA scheme cannot outperform its OMA counterpart is obtained in closed-form, by considering impact of user pairing. Furthermore, asymptotic analysis shows that the aforementioned probability can approach zero under some given conditions in the SNR regime, indicating that the energy efficiency of the proposed scheme is almost surely higher than that of OMA for these given conditions. Numerical results are presented to verify the analysis and also demonstrate the benefit of applying HSIC compared to FSIC.