Green Internet of Things (IoT) aims to enable a sustainable smart world by making energy efficiency (EE) the main performance indicator for IoT hardware and software. With respect to network design, this implies in developing energy-efficient communication protocols and network architectures adapted to the ubiquitousness of the IoT machine-type devices (MTDs) and the sporadic traffic generated by them, keeping a low power consumption at the MTDs-side. In this sense, reconfigurable intelligent surfaces (RISs) have presented the capacity of significantly improving the network coverage using mostly passive reflecting elements, drastically reducing the power expenditure. In this paper, we develop a realistic power consumption model and an expression for the overall system EE for RIS-aided IoT networks that adopt a two time-scale random access (RA) protocol to handle the uplink transmissions. Specifically, during each time slot of the RA protocol, the RIS covers a specific area of interest in the communication cell with a predefined set of phase-shift configurations, changing the channel qualities of the contending MTDs. Numerical results comparing the RA protocol performance reveal that access policies that exploit information of the channel qualities are suitable for green IoT networks, simultaneously attaining competitive EE and throughput combined with low power consumption at the MTDs-side.