I agree that even if you break the Grand Order on the second week and take the main town, the game doesn't end, but in any case, the opponent is left with at most one available treasure and, without control, they usually still lose on the third week.
Breaking the Grand Order on the second week resets the timer to zero, and there can be significant troop losses. The opponent retreats to a treasure (one), while the player who broke the Grand Order (also without control, on both the second and third weeks) can end up in one treasure, if they don't get bogged down taking the opponent's secondary towns.
I specifically remember a game in Novice mode where the opponent broke the Grand Order, I retreated to a treasure, gathered troops, and returned with an advantage, even though the opponent was simply defeated in their own town and I won.
I remember a game with Toga, where he also broke the Grand Order on the second week, took the main town, I returned from a treasure, pushed Toga back, but then decided to chase his army. Toga entered a treasure from my secondary town, and it ended with my loss.
In other words, breaking the Grand Order on the second week doesn't give an advantage and doesn't often end the game.