You would want to modify the switch wiring so that black is always-hot from the supply, and red is switched-hot coming off the switch.
Then, at the fan, you take the cable from the switch, and you connect black (always-hot) to the supply side of the fan controller. The red (switched-hot) goes directly to the fan's lamp.
You would certainly want to have the light switch control the fan's light, because Code requires that there be a light switch in the room, and it must operate a light.
The black wire from the /3 from the switch goes to the fan control module. The fan control module connects onward to the fan motor wire. If the control module is capable of controlling the light, it'll have another wire for that (blue?) Cap that wire off.