No, that's a very ineffective attempt at waste removal. Since you are diluting it as it drains off, the percentage of waste being removed drops sharply with each new cup full. You'd need to flush something like 300% of the volume of the tank through it with that method to attain a satisfactory water change. What you want to do is remove the old water in its pure form so you are actually removing it effectively, then refill.
If it helps, imagine that tub full of orange juice. Now pour a glass of water in. The first water out will be mostly pure OJ, but every glass after that will be more and more diluted. Think about how many hours you'd have to stand there to even cut the OJ down to 50%.