The answer is actually yes, yes you can still run Kodi on an ATV1.
Hardware video decoding under the
BCHD (wiki) has been removed from official Kodi builds, OE doesn't provide ATV builds anymore, and OSMC hasn't released an official build yet, but you can compile and run Kodi just fine even without modifying the code if you use Crystalbuntu (the predecessor to OSMC) or a custom Ubuntu install. Adding BCHD support back in has been done in unofficial builds (
http://forum.osmc.tv/showthread.php?tid=16811 ), but we have no official Team Kodi support for that anymore.
Even if you don't have a BCHD or it stops working, the old ATV1 is still able to handle a number of formats in software, or can be used as a music player, or even some light emulators along with Rom Collection Browser, etc.
Of course, I wouldn't recommend anyone ever go out and buy an ATV1, but if you happen to have one, why not tinker around with it? Getting old things to work and do new things one of the reasons people got into XBMC/Kodi in the first place :)
EDIT: Also, if you ever decide the electrical usage is not worth it, you can hollow out the ATV1's case very easily and use it for a Raspberry Pi 2 and have enough room for an internal power supply and a couple of 2.5 HDDs or one 3.5 HDD. I have dead ATV1's that I've kept just for the nice case! :D