No, your firearm has to be transported locked twice. If you were going to the range with your car, you would have to have it in a locked case, probably with a trigger lock on it, and put it in the trunk of your car and lock it. You would also have to take the most direct route to and from the range. If you are veering off that, you are not following the rules of the authorization to transport, and you are subject to charges.
On April 28th, 2015. See this statement in context.