That's roughly the way the local hospital wireless LAN works. Anyone can connect, but without a VPN client and the necessary authentication and access, they go nowhere. The 192.168.1.xxx IP address issued by the Linux gateway DHCP server does nothing. Only after authenticating with the VPN server, does the VPN server issue a different
10.214.144.xxx IP address that works.However, you might be trading one roaming problem for another. VPN connections do not do well when roaming from access point to access point. The one's I've tried are even more sensitive to packet loss. Lose a few bytes and they disconnect and renegotiate the entire key exchange cerimony. My guess is about 3-5 seconds delay after losing a few packets. You're going to lose something during the switch between access points. Fortunately, VPN authentication and header modification protection is based on IP addresses and not MAC addresses. Therefore, it should maintain the VPN connection when moving between access points.
There's also the problem of licensing VPN clients, although there are plenty of free ones available. Same with clients for PDA's.
In addition, with useable 192.168.1.xxx addresses assigned to clients, there's a real danger that these clients will turn your access points into their personal game network or something. I've had that happen to me. If you access points offer "client isolation" or something similar, use it.