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I tried to power on the Intel® NUC with a wireless keyboard and it is not possible, you can do it only with a USB keyboard. You can wake the NUC with wireless keyboard but you cannot turn on the unit with wireless keyboard.
In this case you could try that one, unfortunately we don’t have this keyboard to test it here, you can see the tested peripherals we have tried here:
You can try the Harmony Ultimate and it could work for you, unfortunately I’m not able to give you a straight answer about if it will work or not, but if the keyboard has been made to work like it shows at the link you provided probably it will work for you.
Thanks and regards!