No the NAS does not even see the wifi dongle that came with the K600 keyboard however it works fine on the TV.
The K600 dongle, correct me if I'm wrong, is a Logitech Unifying Receiver and it doesn't work like an ordinary bluetooth dongle. It doesn't support any other devices except Logitech's modern peripherals. The NAS not supposed to show this K600 dongle in the external device list but it's to be detected internally in the NAS (check dmesg) and you would just pair it normally with the K600 keyboard. As said previously I have the K400, it comes with this particular dongle. It doesn't show in the ADM external device list except in dmesg but I can use the keyboard just fine with the NAS. I'm also using a no brand air remote keyboard that comes with its dongle but not shown in the ADM external device list, only in dmesg. They all work fine in e.g. Asustor Portal and Linux Center.
I would assume their is no pairing code to input and that you just use the connect feature under the external devices menu?
Yup, no codes, use the connect feature after putting the device in pairing mode. I've also tested some other 4.2/5.0 BLE bluetooth dongles but unfortunately they only work after patching but still no codes involved while pairing. To be clear, only my GBU521 works out of the box without patching.