From what I know, if a team amnesties a player, they cannot bid on him in the following auction. However, if no teams bid on him, that player becomes a free agent. At that point, I think the original team can resign the player, but I'm not 100% sure on that.
In the case of Kobe, it wouldn't even matter. This wouldn't work because it is impossible that no team bids even the smallest amount on him. Even if he makes it public that he won't play for any team other than the Lakers and so no team should bid on him, some team will make a bid just so the Lakers can't resign him.