Will a Wired Only Keyboard connected to an Apple Studio Display Function?

I currently have a MBP M3 Max connected to an Apple Studio Display. When I connect the magic keyboard directly to the Apple Studio Display, I notice it will still connect to the MBP wirelessly, and going to bluetooth settings to forget the device will not stop it from instant rediscovery on my MBP.

If I connect a wired keyboard (of course that is Mac compatible) to the Apple Studio Display, will it work on the MBP, or must all wired only connections be directly connected to the MBP?