That's exactly how the new Gulfstream active sidestick I mentioned above works!
The active sidesticks are not direct-linked mechanically, but rather uses a system of electronic servos via a computer to provide positioning and force-feedback. So an Airbus-style "priority button" can still be implemented if desired -- or alternatively a "split control" configuration can be applied, where in a contention situation each sidestick controls half of the control surfaces a la some Boeings.
The cool thing is that the position and force feedback gradient of each sidestick can be altered in real time. E.g., they can be made more sensitive or smooth during certain phases of flight, or alternatively the feedback can be made stronger when approaching aerodynamic or safety limits. Commands from the auto-pilot also move the sidesticks so they can be observed immediately, reducing "surprises" in cases where the A/P suddenly disconnects.