• The answer to your question is most likely 'Yes'. Different ammo will have different points of impact. The answer lies in the recoil impulse, which makes the barrel start to rise right after ignition. How much barrel rise you'll get is based on the weight of the gun, your grip and the energy contained in the round. So based on this, ideally you should see a vertical pattern start to immerge on a paper target when shooting multiple types of ammo.
So I agree with the others. Simply put, different ammo will usually have a different point of impact. If you need a certain target POI, then standardize on one certain brand of ammo that groups well, and then change out your front sight to align the sight picture with the POI. That's much easier and far less expensive.
• Secondly, I'm wondering why you are shooting so much NATO rated ammo. The CZ can shoot this ammo, but in the next sentence from your manual you are also warned not to make a steady diet of this ammo. It's not good target ammo and it's not especially good SD ammo. So you're needlessly adding extra wear and tare to your gun.
If your ammo needs are that specific, then may I suggest that you would be a good candidate to consider home reloading. It's fun. It's easy. It saves a ton of money. And you can easily tailor your ammo to your gun's precise needs.
Hope this helps.