Intervals of low-quality photoplethysmogram (PPG) signals might lead to significant inaccuracies in estimation of pulse arrival time (PAT) during polysomnography (PSG) studies. While PSG is considered to be a "gold standard" test for diagnosing obstructive sleep apnea (OSA), it also enables tracking apnea-related nocturnal blood pressure fluctuations correlated with PAT. Since the electrocardiogram (ECG) is recorded synchronously with the PPG during PSG, it makes sense to use the ECG signal for PPG signal-quality assessment. (1) Objective: to develop a PPG signal-quality assessment algorithm for robust PAT estimation, and investigate the influence of signal quality on PAT during various sleep stages and events such as OSA. (2) Approach: the proposed algorithm uses R and T waves from the ECG to determine approximate locations of PPG pulse onsets. The MESA database of 2055 PSG recordings was used for this study. (3) Results: the proportions of high-quality PPG were significantly lower in apnea-related oxygen desaturation (matched-pairs rc = 0.88 and rc = 0.97, compared to OSA and hypopnea, respectively, when p < 0.001) and arousal (rc = 0.93 and rc = 0.98, when p < 0.001) than in apnea events. The significantly large effect size of interquartile ranges of PAT distributions was between low- and high-quality PPG (p < 0.001, rc = 0.98), and regular and irregular pulse waves (p < 0.001, rc = 0.74), whereas a lower quality of the PPG signal was found to be associated with a higher interquartile range of PAT across all subjects. Suggested PPG signal quality-based PAT evaluation reduced deviations (e.g., rc = 0.97, rc = 0.97, rc = 0.99 in hypopnea, oxygen desaturation, and arousal stages, respectively, when p < 0.001) and allowed obtaining statistically larger differences between different sleep stages and events. (4) Significance: the implemented algorithm has the potential to increase the robustness of PAT estimation in PSG studies related to nocturnal blood pressure monitoring.