Well, that's not entirely true. The question should be: "Can you update your AR's firmware via Code Manager or Code Manager DSi? And does it work on a 3DS?" If you can answer yes to the first question and no to the second, then there's a good chance it's supported, otherwise it's most probably NOT supported.
Anyways, for anyone wondering, here's a quick list of all the ARs that are confirmed working and not working for NTRBoot.
WORKING:
Action Replay DS (no card slot, aka "slim". Might require a firmware mod in order to work.)
Action Replay DS ("fat", aka the one with a card slot)
Action Replay DS EZ
Action Replay DS Media Edition (requires a different installation method than other ARs)
Action Replay DSi (the original one that WON'T boot on a stock 3DS and is updateable via Code Manager DSi)
NOT WORKING:
Action Replay DS/DSi Updates (there seems do be different variants for those, check your ARDS's label if it says "Updates". Also, those are able to boot on a stock 3DS.)
Anything that doesn't come with an USB port or is not updateable, such as Action Replay Ultimate Cheats for Pokémon.
Action Replay Powersaves
I don't own all of these, but I've been able to find out which ones do and don't work by looking at their firmwares (if available). If I'm wrong on anything, let me know and I'll fix this post.