I don't think the Earth Dragon Balls have enough power in them to do such a thing, since they are limited by the overall power of their creator. And I don't think Kami (or Dende) have the oomph to force the Life Entity to grant Batman a white lantern ring and make him one.
He'd need the Super Dragon Balls to make such a wish, or just skip the middle man and kill Goku directly. But those are scattered across two different universes, each one of them is the size of a planet (7,196.2204 kilometers in diameter with a volume just under half that of the planet Neptune), and can only be used by those capable of speaking the language of the gods. So yeah, I don't think Batman's getting White Lantern powers.