Short answer: No. Classic Shell under normal circumstances and use should not cause any Windows slowdowns or affect Windows performance or stability in any way. It does not do permanent or dangerous modifications to Windows files on the disk, but loads only into memory (inside Explorer.exe). It does not even touch Windows settings, all its modifications are done by its own code. When you exit/disable it, original Windows functionality is restored. If you encounter any crash or slowdown, you can report it and it can be fixed.

Long answer:
Classic Shell is like a regular desktop app that you would install on Windows e.g. Firefox, or Google Chrome or Notepad++. It requires some resources obviously to run like any other replacement Start Menu app, however it's very small in size, and is written with performance in mind. Even on my 10 year old laptop it runs extremely fast. All its components are coded in C++ unlike the Windows 10 menu which seems to be using managed code languages for its application logic.

So putting Classic Shell on any version of Windows should not slow it down in any way. Also it uses documented APIs, is a cleanly written app, not some dirty unstable hack which would harm the OS or affect the rest of its functions negatively.

The changes Classic Shell makes are immediately reverted when its processes stop running. It does not do any permanent or dangerous modifications to Windows system files or Registry settings. The Start Menu process injects a DLL into the Explorer.exe process to keep itself running. The Explorer addons can also be disabled using Internet Options Control Panel.