In this paper, we analyze a Cognitive Radio-based Internet-of-Things (CR-IoT) network comprising a Primary Network Provider (PNP) and an IoT operator. The PNP uses its licensed spectrum to serve its users. The IoT operator identifies the white-space in the licensed band at regular intervals and opportunistically exploits them to serve the IoT nodes under its coverage. IoT nodes are battery-operated devices that require periodical energy replenishment. We employ the Microwave Power Transfer (MPT) technique for its superior energy transfer efficiency over long-distance. The white-space detection process is not always perfect and the IoT operator may jeopardize the PNPs transmissions due to misdetection. To reduce the possibility of such interferences, some of the spectrum holes must remain unutilized, even when the IoT nodes have data to transmit. The IoT operator needs to decide what percentage of the white-space to keep unutilized and how to judiciously use the rest for data transmission and energy-replenishment to maintain an optimal balance between the average interference inflicted on PNPs users and the Quality-of-Service (QoS) experienced by IoT nodes. Due to the periodic nature of the spectrum-sensing process, Discrete Time Markov Chain (DTMC) method can realistically model this framework. In literature, activities of the PNP and IoT operator are assumed to be mutually exclusive, for ease of analysis. Our model incorporates possible overlaps between these activities, making the analysis more realistic. Using our model, the sustainability region of the CR-IoT network can be obtained. The accuracy of our analysis is demonstrated via extensive simulation.