Extensive attention has been given to the use of cognitive radio technology in underwater acoustic networks since the acoustic spectrum became scarce due to the proliferation of human aquatic activities. Most of the recent studies on underwater cognitive acoustic networks (UCANs) mainly focus on spectrum management or protocol design. Few efforts have addressed the quality-of-service (QoS) of UCANs. In UCANs, secondary users (SUs) have lower priority to use acoustic spectrum than primary users (PUs) with higher priority to access spectrum. As a result, the QoS of SUs is difficult to ensure in UCANs. This paper proposes an analytical model to investigate the link connectivity and the probability of coverage of SUs in UCANs. In particular, this model takes both topological connectivity and spectrum availability into account, though spectrum availability has been ignored in most recent studies. We conduct extensive simulations to evaluate the effectiveness and the accuracy of our proposed model. Simulation results show that our proposed model is quite accurate. Besides, our results also imply that the link connectivity and the probability of coverage of SUs heavily depend on both the underwater acoustic channel conditions and the activities of PUs.