In this work, performance of a simultaneous wireless information and power transfer (SWIPT) enabled cooperative cognitive radio sensor network (CRSN) is explored over generalized Nakagami-m faded channels. A time switching (TS) protocol for SWIPT is used and the impact of TS factor on energy harvesting and information transmission phases, and information processing and broadcasting phases are considered. The cooperative CRSN consists of a pair of primary nodes (PNs) and sensor nodes (SNs), where one of the SWIPT enabled SN provides cooperative relaying for PNs communication by utilizing amplify-and-forward protocol. The overlay spectrum sharing protocol is used at the SN, which supports PNs communication along with its own transmission and resolves the spectrum scarcity issue. The impact of a non-linear power amplifier (NLPA) is also considered on the network performance. The analytical expressions of outage probability (OP), asymptotic OP, system throughput, and energy efficiency are obtained over Nakagami-m faded channels for arbitrary m. Further, the analytical expressions of ergodic capacity (EC) and asymptotic EC are obtained. The impact of NLPA and other system parameters on the performance of the considered network are highlighted. Finally, the obtained analytical expressions are validated through Monte-Carlo simulations.