back when i was working on jaguars (XJ8 mostly for a while), i changed a lot of small cartridge style water pumps with plastic impellers that had shattered, and (again, in my experience) no, the plastic does not dissolve. If it did, it would not be a suitable material for an impeller in the first place. where all the fragments of impeller ended up, there is no way to know, but many vehicles had odd cooling issues after a pump went bad and grenaded.
And a cast iron impeller will not fail, except perhaps by corrosion, and we've covered that angle well enough.