As you would expect with a modern thin client with a proper BIOS there should be no issues with running Linux on the t610. Tiny Core 7.2 booted from a USB pen drive without any problems as did Tiny Core 10.1.
There is an issue with the amount of Memory available to the OS depending on the size of the Video buffer. See the section Missing Memory under the Firmware tab.
In August 2019 I heard from Mateusz who had had no problems ...running most popular Ubuntu versions, 14.04, 16.04, 18.04 and 19.04.
I also heard from Luca who has fitted his t610 with a PNY 120GB SSD. He has installed various OSs and has the following observations:
xubuntu 19, lubuntu 19, puppy bionic 8, mint xfce 19 all work well but, if I have many windows open and try and watch something on YouTube, the system can freeze and need a reset. With only a few windows open, or only one window plus Youtube, everything is fine.
Linux Mint xfce 9 (my favourite) works but without a network - the required driver isn't part of the standard distribution.
Mint LXDE 13 also works but the browser is rather out-of-date.
I also use Windows Embedded 7 with installed browsers Chrome and Firefox ver. 65
On Xubuntu 19 (using Wine) and Windows 7 Embedded I have a dosbox and all can run all sorts of old games. A great plus here is that the t610 is totally silent - no whirring fans.
With Windows Embedded 7 I've installed VLC + Winamp + Izotope Vinyl and use it as a media center for listening to music and watching movies including HD movies.