A heterogeneous cellular network (HCN) comprising macro-base stations (MBS) and pico-base stations (PBS) is deployed to accommodate the increasing demand for high data rates and improved performance. In anticipation of sixth-generation (6G) networks, non-orthogonal multiple access (NOMA) emerges as a key technique to enhance spectral efficiency and support a large user base. To boost power efficiency and reduce outage probability, base station power amplifiers often operate near saturation, resulting in non-linear distortions (NLD). This study investigates the performance of NOMA-enabled HCNs (HCN-NOMA) under the influence of high power amplifier (HPA)-induced NLD, employing a stochastic geometry framework. Specifically, the impact of imperfect successive interference cancellation (i-SIC) is analyzed and benchmarked against orthogonal multiple access (OMA) in multi-tier HCNs. Performance is evaluated in terms of outage probability, ergodic capacity, system throughput, and energy efficiency. Results reveal that NOMA offers performance improvements of up to 96% over OMA in the non-linear HPA region. Notably, even under i-SIC, NOMA achieves gains up to 93% compared to OMA, highlighting its robustness under practical impairments.