Regardless - Your Furnace NEEDS a outside source (fresh air intake) of air brought in to the furnace to work. If you wire the radon fan to shut down when furnace kicks in - you still need fresh air intake for the furnace to properly vent. 
ETA: thinking about your Radon deal - It's possible you have a negative air pressure deal going on with your home. So, when the furnace kicks on, it is drawing what ever air is in the home (basement) and that in turn is sucking Radon up from below the concrete. Radon is heavy and generally will sit at the lowest level. But, if the furnace need draft, it has enough draw to pull radon gas's upward into the home . . . . . .