GE switch or similar - with load connected but don't control with physical buttons

No, because master switches of that type are designed to also act as regular non-networked switches even if your home automation hub fails completely, so they always control the load if they are wired to it.

There are people who have wall switches with are not connected to the load and then are used to control other devices like in wall micros or smart bulbs. But that doesn’t give you a way to cut power to the fan as well. Is there a reason just a regular circuit breaker wouldn’t meet that use case?

As far as other options for control of fans with lights, you might take a look at the following if you haven’t already: