An object in "free fall", certainly IS accelerating. For objects that jump out of aircraft or fall off the edge of tables, anyway.
If the object is equiped with an accelerometer, it detects no acceleration because the acceleration it is actually undergoing offsets the deflection of the sensor element which normally occurs because of gravity. That is why an accelerometer reads 0 when it is in free fall. It doesn't mean that it is not accelerating, though.