This is the reason why they re-signed Naz Reid to a multi-year deal. They needed a backup when things like this happened, and it happened so they will give more time to Reid for sure. Kind of unfortunate that KAT got injured, but this is the time for Reid to showcase himself "again" as he will be given more minutes. For me, he's one of the best role-player bigs out there, and he can give you an average of maybe 8-10 PPG and around 5 RPG, a good defender, and can stretch the defense with his ability to shoot threes as well.
Reid might not be as dominant as Towns in terms of offense, but he can still be a big help for the team. As for the Timberwolves and their playoff run, as you said, I don't know if they will be a good playoff team without KAT because losing a player who can score an average of 20 PPG every night is kind of demoralizing. They still got ANT though, and other role players must step up on offense on the playoffs.
Yep, losing a player like KAT because of injury is very bad news for the Wolves. I think the remaining games in the regular season will show whether the Wolves can adapt or not. If they start losing games and lose the top spot in the Eastern Conference standings, it can be concluded that they are unlikely to have any success in the playoffs without KAT.