I just tested to double confirm the same w.r.t Private AKS clusters & AKS with authorized IP ranges.
It does work perfectly with that feature i.e. dynamic allocation of IPs.
To answer your question:- "As the Pod subnet is coming from the same VNET , hence control plane communication will not impact even if you are using the Authorized IP ranges, and the feature also works with Private AKS clusters."
Regards,
Shiva.