It's a horrendous situation for the player and I hope that a decent resolution is found.
If transfer didn't go through, then clubs may well fight over the registration, in a who loves Homer more kind of way, could get ugly quickly. Leicester are going to be left in limbo without cover for Drinkwater for 6 months and the only courses of action will be to try and return him to Sporting to get money back or sit and wait it out.
As far as I'm aware, I would imagine transfers to be dependent on registering for the new club, so Sporting may have little choice than to accept him back and return money. I have the feeling if this was a Mbappe, Neymar, Messi type name, authorities would probably find a way to compromise.