If you can work without baud control and without the serial port status lines, there should be a solution.
Correcting myself (I used wanted to know and googled myself) there is client/server software pair that can be used for your purpose, with baud control etc.
I didn't test, but the docs look good - try getting the "sredird" package for running on the thin client, and there is a (Debian only?) package called "cyclades-serial-client" that maps a remote network socket (RFC-2217-compatible) to a pseudo (serial) tty on another Linux box.
If you get this to work, a short report would be nice, as implementing this in LTSP could be of help for other people too.
HTH,
Anselm
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