Is exaggeration a valid way to win an argument?

It very much depends on what you mean by winning the argument. If your intention is just to shut your opponent up and end discussion, that is one thing. If you intention is to intelligently persuade your opponent (or the audience) to see, or even accept your point of view, that is another. It also is a different matter if you are trying to "win" the argument just for the sake of winning, even if you are not convinced that your position is true. Exaggeration and lying can be too quickly confused.