The answer to your question is yes, it should work. If you have already decided not to use standard 9 VDC wall adapters and want to power the device from a higher voltage (15 – 30 VDC) please make sure that you choose a power supply of high quality. Some power supplies can produce voltage peaks significantly higher than the declared output voltage, especially during connection and disconnection. While the device is designed to accept input voltage of up to 30 VDC peaks, high voltage power supplies can harm the device. If you want to use high voltage power supplies it is recommended to also use additional safety equipment to suppress voltage peaks from the power supply.
Though the device can be powered over an Ethernet port it is not compliant with the IEEE 802.3af-2003 standard. Therefore, powering the device from an IEEE 802.3af-2003 power supply will damage the device as it is not rated for input voltages of the PoE standard. The device is also not compliant with the IEEE 802.3at standard, meaning it can't power other devices over Ethernet. You can find more information on RUT routers' powering options here.