Yes, the use / store switch will shut off the refrigerator.
Considering that gasoline Vapors are heavier than air, most folks are unaware of the closest point of combustion. The catalytic converter with internal temperatures exceeding 2000 degrees,has external temperatures up to 1000 degrees Fahrenheit which far exceeds the flashpoint of gasoline Vapors or the distant protected Flame in your refrigerator which is at a height unlikely to be reached by gasoline Vapors.
While RV propane fires a rare but have occurred they are more likely due to component failures versus fueling procedures.
There is a much greater incidence of dangerous gasoline and engine fires. My cousins half sisters step son had his tow vehicle destroyed in a gasoline engine fire. So that this will never occur to me I am removing the dangerous gas tank and engine in all of my tow vehicles.