Recent studies have shown that edge AI deployment requires neural architectures that are simultaneously accurate, computationally efficient, and hardware-deployable. Hardware-aware Neural Architecture Search (NAS) can address this challenge. However, existing works often incorporate quantization directly into the NAS loop, which increases search complexity and tightly couples architecture and quantization design. This paper proposes a three-stage pipeline: a hardware-agnostic Pareto rank surrogate frontend, a quantization bridge with Pareto-aware filtering and feedback control, and an evolutionary Domain Space Exploration (DSE) backend for optimal hardware mapping. An empirical study characterizes how INT4 Post-Training Quantization (PTQ) perturbs the NAS-Bench-201 Pareto space and demonstrates that an FP32 zero-shot surrogate outperforms a dedicated INT4-trained surrogate in Pareto space coverage. Blogger's Review: This paper addresses important issues in NAS and quantization for edge AI, providing in-depth analysis and empirical study on the effects of quantization on the Pareto space, and offering significant reference value for future edge AI development.