The J body model lacks the medal hook, so no, it won't show the medal. Not unless someone adds the hook to the model.
There is a script that causes you to equip a robe, k_donrobe:
void main() {
object object1 = CreateItemOnObject("g_a_jedirobe01", GetFirstPC(), 1);
ActionUnequipItem(GetItemInSlot(1, OBJECT_SELF), 0);
ActionEquipItem(object1, 1, 1);
}
However, you don't swap your equipped gear when you just warp into the module. It doesn't appear that the script is called either in the module's OnEnter or via the only DLG, nor is it referenced in any of the module's other scripts, so I'm not sure what fires it. That aside, it would be easy enough to alter the script to have it do nothing, or perhaps add a conditional to skip doing anything if the Starforge Robes are equipped (I think you can do that, but someone more knowledgeable about scripts would need to chime in).