Probably… It would depend on the exact devices being used. But I’m not sure you’re going to get the effect you want because do you want the light to come on every time the fan comes on? What about at night when you’re going to bed?
If it was me, I would probably stick a battery operated switch for the light on the wall next to the fan switch. The Cooper 9500 would work. You could also use one of the smart switch covers without putting it over an existing switch, just putting it flat on the wall. So the Osram or the gocontrol. All three of those would work with any micro that was controlling the light.
You can use a double gang plate over a single gang switch and put the fan switch on one side and one of the battery-operated switches on the other if you like.
Or you can use the Hue dimmer switch with a smart bulb.
Anyway, @dalec did a project with a similar outcome and knows a lot about wiring, he’d probably have much more to say.