When we talk about bankroll management, it is often in terms of having enough reserves to absorb the variance while playing at an appropriate buy-in. However, you are bringing up a very vaild point. If a person is serious about winning, I would say you absolutely HAVE to know how much you are winning or losing (unless you have soo much money that you'll never run out
).
My cousin is a good player, but he plays higher than he can sustain. He takes shots, busts out and makes new deposits fairly regularly. I am sure he has no clue how much money he has lost. Going along with that, he has a hard time identifying the holes in his game. When he is winning, he feels like the best player in the world, but like Mike "the mouth" he bust out more than he should. (disclaimer, when he is winning, he is better than I am)
Money is the measure of winning and losing in the long run. In any game, if we don't know if we are winning or losing (again, in the long run), it would be pretty hard to know if we were playing well.