Fallout 1 was released with a deadline of 150 days (+100 if you did something specific). This was very controversial, both on the team and with fans. It turned out it made players sense urgency and would rush through the game, which in turn would make people miss a lot of the contents as it was always about rushing through tasks rather than exploring options. The first patch update removed the time limit because people should have time to enjoy and explore the game.
I kind of suspect The Headmaster would suffer the same fate. Currently it's a fairly laid back game with no deadlines and if you screw up, you can just continue and try again later. You can always grind money, grades etc regardless of how long it takes to reach a certain milestone. Adding a time limit will ruin that and I fear it will cause people to savegame scam and focus too much on "get there" rather than enjoying the game.
TL;DR: don't add time limits or deadlines. They will likely hurt more than they will add.
I kind of suspect The Headmaster would suffer the same fate. Currently it's a fairly laid back game with no deadlines and if you screw up, you can just continue and try again later. You can always grind money, grades etc regardless of how long it takes to reach a certain milestone. Adding a time limit will ruin that and I fear it will cause people to savegame scam and focus too much on "get there" rather than enjoying the game.
TL;DR: don't add time limits or deadlines. They will likely hurt more than they will add.