Sure, in the very short run (starting from absolutely no knowledge of the game) you'd have to make mistakes to learn anything at all. But the process of getting better is a gradual decrease of the frequency of those mistakes. You'd want to minimize your mistakes as much as possible as you got better, because the frequency of mistakes will be strongly correlated with how much you lose.

Mm, that all sounds like it's true if you only play games against the same skill level of opponent. If you increase the difficulty level at the same speed that you gain speed, then you won't start winning more games. I guess it's true that you'll stop making some mistakes, but in addition, some things that previously weren't mistakes will become mistakes.

In any case, I guess it's certainly true that there are things you can do that will both decrease the number of mistakes that you make and increase your rate of learning, such as paying more attention.