No, breaker injection testing will not damage your breakers. Testing ensures that breakers will trip at the set current and time prior to a failure, preventing potential injuries, damage, and shutdowns. We have an analogy for understanding the purpose of breaker injection testing:
Imagine you're a baseball player. You have an amazing baseball bat that helps you hit well. You practice batting regularly at the batting cage, making sure that your bat works and your swing feels good. If your bat is working, you'll use it in the game. If it's damaged or worn down, you'll replace it with a new one that does work. You do this because it's better to know that your bat isn't working at batting practice, rather than the bottom of the 9th inning.
Your bat is the breaker. Batting practice is the breaker injection test. And the 9th inning of the game is your operation. It's better to know when your equipment isn't working in a controlled environment, instead of during working hours.