I would not expect it and did a short check on wiring diagrams to find none obvious.
My solution when adding a fan, was to go to the nearest ceiling light, even though it was on a wall switch. My solution was to add a switch on the light body to allow using the wall switch to turn power on for both fan and light and then use the switch on either to control which or both we wanted on.
When you remove the inside trim from the vent you are likely to find solid foam insulation and to find if I could really expect to fish a wire between the light and vent area, I sharpened a 1/4 inch wood dowel and forced it into the foam at the small hole at the light until it came out at the vent. Hint, better odds of finding the 12 inch opening from the small than the other way! For my first try and going to another unswitched light, I got within 6-8 inches before hitting a solid metal cross member in the ceiling!
We find we like to add the fan in the front where it is less prone to bother us than if over the bed, so we turn it on and open windows in the bedroom for air to enter.
2015 Winnebago Vista 31KE on 2014 chassis