Nothing connects the Star Wars galaxy with ours (the Milky Way), other than that Humans have developed in both, but this coincidence has never been implied to be anything other than independent evolutionary processes. However, if we are to consider a crossover between Star Wars and E.T. based on the mention of Brodo Asogi and its extra-galactic expedition, we can infer the following: the Brodo Asogi Senator, Grebleips, sent an expedition to another galaxy. This may have been our galaxy, and we can assume that is how E.T. ended up on Earth. The movie says that E.T. is a being three million light years from home (our galaxy is approximately 100,000 light years wide and its closest neighbor (Andromeda) is approximately 2.5 million light years away), so his home planet has to be in another galaxy other than the Milky Way or Andromeda, perhaps the Star Wars galaxy. E.T.'s home galaxy would therefore be part of the Local Group and the Virgo Supercluster at approximately a megaparsec away from us. However, this would mean, E.T.'s home galaxy (and, possibly, the Star Wars galaxy) would not be, on a universal scale, a galaxy far, far away but one of approximately forty galaxies that are our "neighbors". In any case, the fictional Star Wars galaxy is (at least theoretically) on the same plane of existence as ours, as it is a supposedly finite distance of "far, far away" from the Milky Way.
That would suggest that the light from the Star Wars galaxy would reach Earth roughly 3 million years after the events in Star Wars. Unless the ET species has lived for more than 3 million years after the events of Star Wars, we can assume that the light from that galaxy has yet to reach us.