Deep learning techniques have shown promising results in the automatic classification of respiratory sounds. However, accurately distinguishing these sounds in real-world noisy conditions remains challenging for clinical deployment. In addition, predicting signals with only background noise may reduce user trust in the system. This study explores the feasibility and effectiveness of incorporating a deep learning-based audio enhancement step into automatic respiratory sound classification systems to improve robustness and clinical applicability. We conducted extensive experiments using various audio enhancement model architectures, including time-domain and time-frequency-domain approaches, combined with multiple classification models to evaluate the module's effectiveness. The classification performance was compared against the noise injection data augmentation method. These experiments were carried out on two datasets: the ICBHI respiratory sound dataset and the FABS dataset. Furthermore, a physician validation study assessed the system's clinical utility. Integrating the audio enhancement module resulted in a 21.9% increase in the ICBHI classification score and a 4.1% improvement on the FABS dataset in multi-class noisy scenarios. Quantitative analysis revealed efficiency gains, higher diagnostic confidence, and increased trust, with workflows using enhanced audio improving diagnostic sensitivity by 11.6% and enabling high-confidence diagnoses. Incorporating an audio enhancement algorithm boosts the robustness and clinical utility of automatic respiratory sound classification systems, enhancing performance in noisy environments and fostering greater trust among medical professionals.