CYOA is short for Choose your own adventure, if anyone on here didn't know.
Anyway, would it be possible? Has anyone ever tried it before? I mean, action games can be made, so why not.
Absoutely possible. The only real difference between a CYOA and a standard adventure game is that, instead of writing one long well-crafted story, you have to write maybe three or four longish stories and a ton more "mini"stories. Of course, unless you have very modest goals, this could easily lead to tripling or quadrupling the workload of your game, so it could be difficult to execute the idea.
However, if you browse around the forums a bit, you'll find that an esteemed gentleman named Snake is already working on a CYOA-style game.
I recommend you download AGS, read through the manual, and get to it, young man!
Good luck, etc. etc.