[RJ]

Hello and welcome to PC Mech.
No, you won't damage the computer if you put in a damaged hard drive.
Otherwise every hard drive would be a potential danger. .. as they could fail any time.

To be really sure if the thing is broken (it's normal that they run very hot.. .. but clicking sounds ain't a good sign) you can download a diagnostic tool (every hard drive manufacturer provides such a tool, just go to your hard drive's manufacturer and download it) and run it. The tool will tell you if, and what exactly, is broken.

RJ