If your PurePower 2000 is the same one that a friend of mine has, it has a battery that stores energy such that the incoming AC is not fed directly to the equipment, but stored in the battery first and then supplied to the components. If that is the case, different power cords from the wall to the PurePower should make no difference.
However, high-quality aftermarket power cords from the PurePower to your components will make a big difference as we experienced first hand a couple of weeks ago when we experimented with several high-quality aftermarket power cords (one PS Audio and two different Synergistic Research lines). Each cord made a significant change in the sound of his system. He ended up buying a Synergistic Research Precision AC to feed his Modwright preamp from the PurePower 2000 and using the PS Audio power cords to feed his Carver monoblock tube amps, again from the PurePower 2000.
However, high-quality aftermarket power cords from the PurePower to your components will make a big difference as we experienced first hand a couple of weeks ago when we experimented with several high-quality aftermarket power cords (one PS Audio and two different Synergistic Research lines). Each cord made a significant change in the sound of his system. He ended up buying a Synergistic Research Precision AC to feed his Modwright preamp from the PurePower 2000 and using the PS Audio power cords to feed his Carver monoblock tube amps, again from the PurePower 2000.