As far as I can tell the question is about the "taping injuries" speciality. This only affects players that are injured during the current game, at the time the game is baing played. If that player was injured and the duration was to be for that game only, then a doctor with that speciality has a chance of healing the player during the game so the player can make a dramatic return to the game. As far as I know it has no effect at all on anything between games.
I have also read that once a player is injured that if you buy a new doctor it has "close to no effect". I don't know if that was just someone just wildly speculating but I have never heard it mentioned as a good idea to get a new doctor to treat an existing injury.