Machine learning has been extensively applied for classical software testing activities such as test generation, minimization, and prioritization. Along the same lines, there has been interest in applying quantum machine learning to classical software testing. For example, Quantum Extreme Learning Machines (QELMs) were recently applied for testing classical software of industrial elevators. However, studies on QELMs, whether in software testing or other areas, used ideal simulators that fail to account for the noise in current quantum computers. While ideal simulations offer insight into QELM's theoretical capabilities, they do not enable studying their performance on current noisy quantum computers. To this end, we study how quantum noise affects QELM in three industrial classical software testing case studies, providing insights into QELMs' robustness to noise for software testing applications. Such insights assess QELMs potential as a viable solution for software testing problems in today's noisy quantum computing. Our results show that QELMs are significantly affected by quantum noise, with a performance drop of 250% in regression and 50% in classification software testing tasks. Quantum noise also increases uncertainty in QELM models, producing a saturation effect where larger qubit counts make the models increasingly random and unreliable. While error mitigation techniques can enhance noise resilience, achieving an average 3% performance drop in classification, their effectiveness varies by context. For classification tasks, QLEAR performs well, whereas Zero Noise Extrapolation is more effective for regression and smaller qubit counts. However, no single mitigation approach consistently reduces uncertainty across tasks or scales reliably as the number of qubits increases, highlighting the need for QELM-tailored strategies.