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Machine learning has been extensively applied for various classical software testing activities such as test generation, minimization, and prioritization. Along the same lines, recently, there has been interest in applying quantum machine learning to software testing. For example, Quantum Extreme Learning Machines (QELMs) were recently applied for testing classical software of industrial elevators. However, most studies on QELMs, whether in software testing or other areas, used ideal quantum 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 and real-world classical software testing case studies, providing insights into QELMs' robustness to noise. Such insights assess QELMs potential as a viable solution for industrial 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 tasks and 50% in classification tasks. Although introducing noise during both ML training and testing phases can improve results, the reduction is insufficient for practical applications. While error mitigation techniques can enhance noise resilience, achieving an average 3.0% performance drop in classification, but their effectiveness varies by context, highlighting the need for QELM-tailored error mitigation strategies.