"Jim Rojas" wrote
I took it apart and ran water through the heat exchanger. The engine stays
cool. I also ran water downwards to the intake, and it flows. If I use the
muffs and try to pump water up, there is no continuous flow at all.

There aren't a whole lot of things that can go wrong with that type of pump.
If it isn't pumping water and there's no obstruction in the line, the base
gasket could be installed incorrectly or the key that locks the impeller to
the shaft could be missing. It may also be possible for the cylinder liner
that the impeller rotates in to spin inside the housing, but I've never seen
that happen.

Regarding the original question, anything's possible, and I know firsthand
what a PITA it is to have to dissassemble a drive unit that you just put
back together, but when all is said and done it would be easier, cheaper,
and more reliable to fix the pump than to cobble together a closed cooling
system.