For a simple exhaust fan which only did on and off, sure. The problem is that you have a variable speed fan. The physics are different. There’s a reason why the manufacturer and the seller say in bold type in the instructions that it should not be used with a ceiling fan.
There are also people who have posted Amazon reviews saying that they tried it with fans and the switch burned out. That’s a fire hazard.
With fans it’s not just a matter of the total power being drawn, it’s the method of regulating that draw. This has been discussed in the past regarding a number of different devices and fans.
GE and Leviton both make variable speed fan control zwave switches which work with SmartThings. There is also a zigbee device which is popular. You would need to check the specs on those to see if they match your whole house fan.
Have you had a chance to look at the fan FAQ yet? (This is a clickable link.)