Recently, ambient backscatter-based communication is considered as an appealing approach, which enables energy-constrained nodes to transmit by backscattering ambient signals, and it has the potential of being integrated with RF-powered NOMA network. In this paper, we analyze the outage performance of a two-node system that works on ambient backscattered signal. One energy harvesting relay, working in time switching relaying (TSR) mode, which assists the transmission of NOMA signal of two users, acts as a backscatter device (BD) to transmit its information to a closely located IoT node by backscattering the signal received from two users. The IoT node transmits its information to the relay by backscattering the signal while the relay transmits downlink NOMA to two destination users. We evaluate the outage performance of backscattered signal at the relay and IoT node. System outage of the NOMA users and throughput of the backscattered transmission are also derived. The effect of backscattering factor on individual and system outage of NOMA users, outage of BD users, and backscattered throughput is indicated. Further, we show the impact of time switching factor on outage and throughput of backscattered network. Ergodic capacity of backscattered network is also evaluated.