Possibly. In your other post
HERE you mention a knocking sound. I've heard water pumps make a knocking noise when they fail, I've also heard the cooling system make a knocking noise when it's overheated.

I've also known water pumps to make no noise... and fail.
I guess you could take you could take the pump off and have a look at it/listen to it.
Allans Garage retired. Try PGS (Plymouth Garage Services) or Mayflower Auto Services Plymouth