Re: possible water pump?
I have a 2006 Merc 25 4 stroke that I purchased with a similar problem. The impeller was neglected, came apart and there was a piece up the water tube to the the powerhead had to be removed to get it out. I think it was actually pivoting in the tube and the degree of obstruction would vary.
If there are pieces missing off the impeller, I would consider where they went.