You must clearly define the term 'VPN router/network'. A network can consist of a single switch, in which case Kiosk should work just fine out of the box. As for VPN, you need VPN endpoints, which many home/consumer routers are not. They pass the IP frames containing the VPN information, but that's it. If your NioNode network has a VPN endpoint attached to it, which also has access to the network from which you wish to connect from, you will most likely need to modify the pandad configuration file on the Kiosk host in order that it can 'find' the NioNodes as the IP multicast discovery will not work across routers. If you wish to use the Internet, you should make sure you have a static public IP available for this VPN endpoint.
In most cases using a VPN tunnel will not require ports to be forwarded. IIRC pandad uses TCP port 4000, but if you have a correctly configured tunnel, it should pass IP traffic regardless of the Layer 4 payload.
In short, yes it is possible given the correct hardware and network resources.