The diffusion of fingerprint verification systems for security applications makes it urgent to investigate the embedding of software-based presentation attack detection algorithms (PAD) into such systems. Companies and institutions need to know whether such integration would make the system more "secure" and whether the technology available is ready, and, if so, at what operational working conditions. Despite significant improvements, especially by adopting deep learning approaches to fingerprint PAD, current research did not state much about their effectiveness when embedded in fingerprint verification systems. We believe that the lack of works is explained by the lack of instruments to investigate the problem, that is, modeling the cause-effect relationships when two non-zero error-free systems work together. Accordingly, this paper explores the fusion of PAD into verification systems by proposing a novel investigation instrument: a performance simulator based on the probabilistic modeling of the relationships among the Receiver Operating Characteristics (ROC) of the two individual systems when PAD and verification stages are implemented sequentially. As a matter of fact, this is the most straightforward, flexible, and widespread approach. We carry out simulations on the PAD algorithms' ROCs submitted to the most recent editions of LivDet (2017-2019), the state-of-the-art NIST Bozorth3, and the top-level Veryfinger 12 matchers. Reported experiments explore significant scenarios to get the conditions under which fingerprint matching with embedded PAD can improve, rather than degrade, the overall personal verification performance.