If the burns have not healed, no. Mederma is mostly used as a scar reducer and will do little, if anything, to help second-degree burns heal. If the burns have healed you might use it to reduce their appearance.
If it is a healed burn and is now just a scar, there should not be any reason you could not use Mederma. You do not want to use Mederma if the burn is not healed because Mederma is not made to make burns heal. It is made to fade already healed scars.