If it's out of fuel then it can no longer generate any heat. The position of the control rods wouldn't matter, and it couldn't melt down. If you're referring to reaction mass (the hydrogen gas), then yes, you would need to insert the control rods to stop the reaction. Or land the reactor and use it to power your Mars colony.

If you do the latter, then you will have had to build it with another cooling mechanism in mind. That could increase the mass of the reactor and reduce your payload capacity, so you might not do it. Instead, you might include just enough uranium to make the trip, and no more.