Não, de jeito nenhum!
Dê uma olhada em Usando o PuTTY :
PuTTY's copy and paste works entirely with the mouse. In order to copy text to the clipboard, you just click the left mouse button in the terminal window, and drag to select text. When you let go of the button, the text is automatically copied to the clipboard. You do not need to press Ctrl-C or Ctrl-Ins; in fact, if you do press Ctrl-C, PuTTY will send a Ctrl-C character down your session to the server where it will probably cause a process to be interrupted.