it doesn't matter if your wireless controller uses RF or bluetooth, as long a reciever can be plugged in via usb. But even then, it's unfortunately a little more convoluted.

Xbox One (and Xbox 360) both have a controller authentication that is checked when you connect a controller. If the proper authentication response isn't returned, the Xbox will just ignore the controller.

It is possible to connect a foreign controller, but you'll need something that can passthrough the authentication data from an appropriate controller and passthrough commands from a third party controller. I use a CronusMax Plus, which makes it fairly straight forward:

• Step 1: plug in CronusMax Plus
• Step 2: plug in original/licensed Xbox One controller via USB and let authenticate
• Step 3: unplug Xbox One controller and plug in Xbox 360 reciever

Alternatively, you can plug a usb hub into the CronusMax Plus, with original controller in first USB port, and 360 reciever in second port, and CronusMax Plus will take care of the rest so you don't have to unplug anything.

I've used it to connect my Wii U Pro controller (via mayflash adapter, that imitates an Xbox 360 controller) to my Xbox One. And I'm currently on the lookout for an original wired 360 controller, so I can do the same thing on my 360.

Edit: there is also the Cronus Zen, which is apparently the new flagship device. I haven't looked into it, since I already have a CronusMaxPlus, but it appears to basically be the same, but with a built in usb hub and bluetooth, so you don't need to unplug.