No, even setting it up with the same height, camber, caster, etc. values, the kart will behave differently. In fact, the chassis used in the two categories is different. For example, in the KZ the bearing housings usually used are higher to increase traction. Additionally, the weight distribution changes.
What mostly varies is the type of driving, as smoothness is preferred in the non-shifter while with shifter karts the driver has more precise handling when deciding what is the right spot on the apex of the line he has chosen. For this reason, it makes no sense to have the same setup with the two types of karts, even with the exact same tires.