If the conductivity in the well is greater than in the formation, could you expect that the water would be gone from within the well above the pump first?

The concept of hydraulic connectivity within the borehole itself being infinite relative to the formation is true. As you start to pump, you are going to get drawdown. You will pull that stored water from the casing or borehole first, blending that into the formation – you will be pulling some water from above, and some water from the formation. At some point the water level will stabilize in the well, and a stabilized head value will be achieved, so then the only water being pulled is the water from the formation.