Can Turbo Booster (3rd Party Application) damage your CPU?

No, using Turbo Boost will not damage your CPU or any other hardware components.

You seem to be confused about how Turbo Boost actually works. When you install a third-party application to disable/enable the Turbo Boost feature, you're not actually enabling the boosting of the CPU. Instead you're enabling the feature where the CPU decides by itself when and if to boost.

So in essence: You're not really turbo boosting all the time, and the CPU will by itself make sure to only turbo boost when it is safe to do so.

The rationale behind the third party applications is mainly to disable Turbo Boost for those that prefer increased battery time over performance.