I have worked with people who fit this description, and I have certainly felt as if my desire to beat them, or at least not be beaten by them, has pushed me to do my best work.
But it's fundamentally an adversarial relationship, and it reminds me a bit of my kids' favorite movie, "Monsters, Inc." You can become so convinced that you need fear to excel that you fail to realize there's a better way.
The people who have TRULY led me to be my best have not been adversaries. They have been supportive mentors. They do everything that the nemeses do, in terms of bringing out the best work in me, but they do it through building up rather than tearing down.
And when I say they do everything the nemeses do, I really mean that. I can't think of any way that a nemesis has led me to grow that couldn't have been also achieved by a strong, encouraging mentor or manager.