My (currently brief) experience here is based on connecting a CDROM drive to the IDE connector:
DSL (4.4.10) boots and runs.
Tinycore (1.4) Ran fine from CDROM.
As it's a conventional Geode GX1 configuration with a normal BIOS (very similar to many other thin clients such as the Neoware Capio) there should be no problems running various flavours of Linux.
Any comments? email me. Last update June 2009