Does the saddle height need to be changed when the crank length changes?
Saddle height for new bike setup purposes should always be set relative to the pedal, not the BB center or any other reference point. So yes, crank length makes a difference.

Using the ground or BB center as a reference point is convenient for re-establishing a given height after the post has been moved, but not for setting up one bike to have the same leg extension as another.