No it would not because a teaspoon is very small and can not practically tell you how much is in it now a graduated cylinder would because it is practical for a carton of milk and it can also tell you how much is in it.
In my opinion, I would not. Most milk cartons are half-gallon or 1.89 liters. One liter is around 200 teaspoons, and so if you measured by teaspoons, your answer would be around 400, specifically, 383.4511 teaspoons.