Lutron Caseta Diva Question - Light that has fan

I have an older house with no Neutral. I used a Lutron Caseta Diva switch on my bathroom (which is just LED Vanity lights and an overhead light which has hue bulbs) and its awesome.

I want to add the same switch to my kitchen lights which has an over head LED and a 3 bulb light with a pull chain fan connected to the same switch. I don’t care if it controls the Fan I just want it for the lights, but I read you shouldn’t use a switch with a dimmer if there’s a fan. Anyone know if this will cause an issue or it the issue it just won’t control the fan?