Background/Objectives: Stress urinary incontinence (SUI) can be masked by pelvic organ prolapse (POP), resulting in so-called latent SUI, and can also worsen postoperatively after POP surgery. Preoperative urodynamic (UD) testing can help identify such hidden dysfunctions, though its routine use and predictive value remain unclear. Material and Methods: This retrospective cohort study included women who underwent POP surgery between January 2019 and October 2025 and who underwent selective preoperative UD and postoperative follow-up (FU). The primary endpoint was to identify urodynamically latent SUI in women undergoing POP surgery, defined as clinical loss of urine during UD with prolapse reposition in patients without preoperatively diagnosed SUI. Secondary endpoints included evaluating de novo SUI rates, incontinence outcomes in women with preoperative UI, and the predictive value of UD for postoperative SUI in asymptomatic patients. SUI outcomes were assessed using validated questionnaires (International Consultation on Incontinence Questionnaire—Urinary Incontinence Short Form, German pelvic floor questionnaire), clinical stress testing, and anamnesis. Results: A total of 261 patients were included. Of those, 70 patients (26.8%) reported SUI, 16 (6.1%) urgency urinary incontinence, and 101 (38.7%) mixed urinary incontinence. Ninety-four patients (36%) received incontinence surgery. Latent SUI was identified in 13 patients (5%): of these, one underwent Burch colposuspension, and two underwent tension-free vaginal tape implantation, while the remaining 10 patients (76.9%) did not undergo incontinence surgery. At FU, 12 of 13 patients (92.3%) were continent; data were missing for one patient (7.7%). De novo SUI occurred in 6 patients (2.3%); these patients did not undergo incontinence surgery and did not show signs of latent SUI in UD. Preoperative UD demonstrated low sensitivity (0–44.4%) but moderate specificity (73.8–77.3%) for predicting postoperative SUI, with high negative predictive values (up to 98%), although these findings should be interpreted in light of the low event rates. Conclusions: In this selected cohort of women undergoing POP surgery, preoperative UD showed limited predictive value for postoperative SUI.