It may help to link to the product.
If it’s a USB device using the HID interface, it is very likely to work with any Linux.
If it’s a wireless device using a USB unifying receiver exposing the HID interface, ditto. (I’m using this and it even works in BIOS.)
Do you own such a device? If so, you want
lsusb -v output for the device. You can also just use the USB vendor id and product id to search the internet to see whether anyone has commented on it as far as Linux compatibility goes.
The only way that anyone could warrant that it does “just work” would be if that person had gone out and bought the device and tested it.