[June 2009] 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.
[September 2012] I connected a Compact Flash adaptor to the 40-pin IDE interface. There is a convenient header nearby that can provide power for the CF adaptor - I used it to provide the 5V required by the adaptor. Tiny Core 4.6.5 booted and ran without any problems.
[January 2018] For my latest checks I installed Tiny Core 8.2.1. onto a 32MB DOM on another thin client and then transferred it to the EON. It ran without any problems.
Any comments? email me. Added June 2009 Last update January 2018