When you say change the public IP, I’m presuming you’re jammed instance is behind a firewall and you’re doing “split DNS”. Changing the IP (either the internal or the external) should have zero impact other than updating internal dns to point to the new ip and updating external dns to point to the new IP). You may have upwards of a day that you are waiting for the external dns to update worldwide but usually it’s not even that long. Just make sure you keep the dns name the same update load balancers if you have them.
While this is not JSS-related, if you have caching servers on your network you may have to tune them a bit if you have them set up with any kind of advanced config, but if they are set up with a standard vanilla config you should be fine. If you do have an advanced config, see this article: https://support.apple.com/guide/mac-help/configure-advanced-content-caching-settings-mchl91e7141a/mac