I'm not sure thin client is what you're lookign for. Thin Client is basically a way of saying "diskless machine". So what happens is you basically have a monitor, keyboard, mouse, and tower with no drives. This machine boots over the network off of some central server. What you really have is one computer with a bunch of monitors, keyboards, and mice. If you're actually interested in thin client, I would recommend trying to use Edubuntu or Skolelinux as a first crack. They'll let you use the same install CD to setup each machine as either a client or server. Then you can modify the packages installed to make it not look like kid computers...
So yes it gives all the computers internet access (provided the server has access), but it isn't really giving individual computers internet access.
If you have a bunch of desktop machines that you want to share internet access, you're looking for a router/NAT setup.