The keyboards does not require Bluetooth to be enabled, however Bluetooth must be turned on for the computer. However, to handle your issue, just because you have a Bluetooth device does NOT mean it can be controlled by your Mac. You need to check with each device's system specifications to verify if it can be controlled by Mac OS.
For example, I own a pair of Bluetooth enabled hearing aides that DO NOT connect to my Mac. They will connect to my iPhone for things like listening to music but not to my Mac for doing the same thing. YOU need to do your due diligence with each device to see if what you want to do is even possible.