In this paper, the energy efficiency of a two-user downlink NOMA system aided by several ambient backscatter devices is investigated. We analyze both the tradeoff and the ratio between achievable rates versus power consumption, assuming that the backscatter devices are in fully cooperative mode. In the case of two backscatter devices, we derive a closedform solution in terms of the optimal reflection coefficients and power allocation policy by exploiting the properties of the energy-efficiency objective and the Pareto boundary of the feasible set. For more than two backscatter devices, the problem becomes difficult and our methodology cannot be extended easily. Nevertheless, we evaluate the performance of NOMA aided by several (up to four) backscatter devices via numerical simulations. Our numerical results show that the energy efficiency of the twouser NOMA system increases with the number of cooperative backscatter devices. Moreover, in the high noise regime, the relative efficiency gain increases with the number of backscatter devices reaching up to 370 % compared to conventional NOMA.