No, that was ret-conned a while ago.
Just before they lower him in, you see a couple of ugnaghts stop in front of him and do something, but because it's at the very bottom of the screen you can't tell what. Han keeps his hands in the same position, so the explanation is that they took the cuffs off him at the last second and he just didn't feel the need to move his hands at that point, since it wouldn't have gained him anything anyway.
As for the strap across his back connected to the bands on his arms, that was explained away as being made of a form of carbonite that melted into the rest of the block, which is why it wasn't there when Leia freed him in ROTJ.