I'm running a small, low power web server chip which creates a Wi-Fi access point using WPA2-PSK AES encryption. This chip is never connected to the public Internet or any other network. A client device may connect to this access point and receive HTTP pages. This is basically like connecting to your router's configuration pages, but the router is not connected to anything else.
My question is, since the only connection is already using WPA2, would using HTTPS instead of HTTP within that connection provide any additional level of security that I'm not already getting with WPA2?