You can change the IP if the name remains the same and the name can be resolved by all your clients (dns or NetBIOS).
If you have clients that do not communicate, just repush the agent to those.
Also consider if you have firewall rules based on that IP and/or proxy rules based on that IP
Is this the same for Agent Handlers? I'll need to re-IP one of ours soon...
That is correct. In either case, regenerate the framepkg.exe once done.