No. It should not "spin" because it is geared to the crankshaft. You might get it to move back and forth a degree or two.

Will a bad water pump still spin?

In most cases, the water pump is binding up, causing the pulley to stop spinning. Replacement of the water pump will fix your problem. The pulley will need to be replaced if there is damage from the belt on it. If there is no damage, then the pulley can be reused.

What does impeller pitch mean?

"Pitch" Explained - "Pitch" Refers to the degree of angle of the impeller blades. Straight pitch impeller blade is angled the same from the front of the hub to the rear. Progressively pitched impellers change angle from the front to the rear.