We're living proof that it's possible. Local school district, using diskless Linux in every school, roughly 95% of all PCs in the district are running Linux. IT budget is just barely over $100,000/year and that includes hardware and software. 14,000 students in the district, spread across ~10 towns, in 50-odd buildings. Only 14 IT staff, looking after it all.
We pay $0 for the OS and 90-odd% of our apps (we pay for a CAD program, a typing program, and some VC stuff).
Computers are diskless appliances, booting off the network, mounting filesystems off the local server, and running all applications locally. Thus, we get all the centralised management of a thin-client setup, but with all the power of a local computer (apps run on the local CPU, using the local 3D graphics card, pumping audio through the local soundcard, etc). Each one is under $200 CDN, with a quad-core Athlon-II CPU, 2 GB of RAM, and either nVidia or ATi graphics onboard.
They are treated as "disposable" appliances -- if one fails, sent it to maint, grab a spare, plug it in, carry on with your day. Replacement time for a hardware failure is under 15 minutes.
4 service desk staff look after 90% of the software side of things from a central office. 5 school techs look after the other 10% of the software onsite, and hardware issues. Then there's a video conferencing tech, a hardware tech, an electrician, some programmers and managers.
We're using Debian on the servers, FreeBSD on the firewalls and backups servers, and Xubuntu on the desktops. $0/desk.
Oh, did I mention we also have NX installed to allow any student/staff member remote access to their full Linux desktop from anywhere? Try that without licensing fees on Windows. :)
We went from paying several hundred thousand dollars per year in software licensing (Novell Netware, Windows, Office, anti-virus, Ghost, etc, etc, etc) to virtually nothing per year. It's been over 10 years now since we started the transition to Linux (2001), and the savings are HUGE!