I should point out that Myrddin is just a different pronunciation of Merlin, and that his family name is traditionally either Emrys or Ambrosius.
Also, King Arthur supposedly was from the 6th Century, while Hogwarts was founded in the 9th or 10th Century. Unless Arthur had access to the Fountain of Youth, or some other means of prolonging his life, Godric was more likely one of Arthur's heirs, not Arthur himself.