Coil whine is in no way harmful for your card, and does not affect performance or longevity. Coil whine is simply the vibration of the coil in an inductor as the power passes through it. On a high end graphics card, ten or more large inductors would help provide power to critical components on the card.

Does coil whine damage your PC?

Coil whine doesn't cause damage nor is a sign of failure. Sometimes it can be silenced by enabling vsync but regardless it is not a problem other than maybe annoying.

Is coil whine a fault?

Coil whine is really nothing to be concerned about. It can be annoying, of course, but it isn't like a rattling engine or a squeaking wheel—the noise is a byproduct of your PC and graphics card's normal operation. Your system isn't losing any performance or longevity because of coil whine.