Does a grenade make a noise as the pin comes out?

Answer 1

No. The pin simply keeps the spoon (handle) on. Once the grenade leaves the hand, the handle (spoon) flies off...that's when you hear the "clanking" noise. You can visually see the spoon separate from the grenade in flight.

Answer 2

I never had that happen. Pulling the pin does nothing other than letting the firing lever pop out as soon as you throw the grenade.

On the other hand, there are practice grenades that you could say were whistling when you release the firing lever, but it is just the sound of the small powder charge going off.

It's possible you might be thinking of artillery simulators. Those make a whistling sound prior to detonation.