One should know the innards of the Grainfather Connect controller.
For instance, does it use a PID logic or does it just lower the power to the heater when the target temperature is approaching? If the Grainfather has some fixed power levels that can be controlled by the controller (for instance, 1 or 2 elements) then the Controller might use that function. Another automatic kettle might have only one element. If it uses a PID logic, the parameters might need some tweaking because of the different shape of the kettle, the different evaporation rate or dissipation rate etc.
Also, The Grainfather might not have its temperature probe at the bottom of the kettle, while most have. Those kettles which have the probe near the heater might safely assume that's the hottest part of the system, and program accordingly. Maybe that's not true for the Grainfather.
If there is only only one heating element in the Grainfather, and the temperature probe is at the same position as the receiving kettle (bottom probably) then it should work fine.