You do not get a double bonus by claiming the other faction's datacron. I confirmed this on Corellia by hopping onto the railway and running all the way to the Imperial landing area and then locating the datacron in that part of the planet.
It gave me the same dialog as though I had clicked on a Republic datacron that I already had; basically "You have already learned the power from this datacron" or something of that sort. Others may say that you are denied access.
Bonus fun fact: The tiny vista that you ride through on the Republic train just before reaching the second adventure area on Corellia is almost identical to the new Black Hole quest area. A couple of the buildings or props have been moved, but the layout is identical. Because of the angle you see it from the train, you can hardly tell.