I don't know if Helicopters apply the same here or not.
A turbine heli hovering inverted would be very similar to what you are describing.
The turbine exhaust would be above the main rotor and the air is being blown down so the hot gases are going thru the rotors.
I have not heard of any negative issues with the carbon main rotors.
You may want to check with Bergen Helicopters to get more info on if this is an issue or not.