Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence within an effective noise modeling framework that challenges this consensus. Through experiments on quantum graph neural networks for molecular property prediction, we observe heterogeneous, initialization-dependent responses within this effective noise modeling framework. Among randomly initialized models with identical architecture, approximately one-third show performance improvement under moderate noise, while a smaller fraction deteriorate and the remainder are marginally affected. We identify a strong negative correlation (r = -0.62) between baseline model performance and noise benefit, suggesting a regularization-like effect for under-optimized models while disrupting well-converged ones. The observed optimal noise level falls below theoretical predictions, indicating error cancellation in structured quantum circuits. These findings suggest that, within the adopted effective noise model, noise effects depend critically on initialization quality and need not be uniformly detrimental, motivating structure- and noise-aware optimization strategies.