You can add them, nothing will happen with the tank, in fact they will help the tank with the added calcium, biofiltration in the long run. However, once placed in the tank they will never appear as they are now. Pristine, white, and clean appearing. Once they are introduced in the tank, they will take on a dirty looking appearance. This is actually good, this means that they are adding to the biofiltration of the tank with bacteria adhearing to the pieces. So this is your decision.
I actually have a few dead coral pieces in my reef, and really like the look of it. Of course, all of this is assuming that the coral never had any copper, or medications used in the original tank.