You could do this with a single server for many raspberry pi systems and simple x forwarding set up (so you'd need X running on the pi). The advantage of this approach is you could run a mix of native and non native applications - with non native applications just being scripts than run ssh -X software, with an account on the server per application. If you wanted a full system thin client, then XDMCP would be a better choice.
Setting up raspberry pi systems as LTSP would be more interesting, and there's already a project to do it. You'd need a LTSP server for this.