I have some recent HP thin clients, and Linux supports 3D acceleration on this hardware.
I have played with LTSP and GNOME 2. I am new to the world of thin clients, and I understand that GNOME 3 requires hardware accelerated client side OpenGL to work well.
How would I best go about getting GNOME Shell to run on a capable thin client as a local app, while launching other apps on the server as normal?
At that point it's not longer really much of a 'thin client', but LTSP 5.2 also offers the capability of operating your terminals as 'Fat Clients'.
In this case, the terminals still boot off the network via the LTSP server, but much of the application work is done on the local workstations.
I'm not sure how feasible it is to implement the way you suggest (which is opposite of what most people are usually trying to do), but it is certainly workable.
Further reading (as of March 2012): https://help.ubuntu.com/community/UbuntuLTSP/FatClients