To answer your question about why are the so called "Idle games" so appealing is actually pretty easy. I think even Extra Credits did an episode on youtube about the toppic.
Games like these are pretty much created in order to scratch our "itch for multitasking" since they require minimal effort to play yet those increasing numbers still give us the satisfying feeling of making a progress. I know I was put off by the candy box since all I saw was a number and a button. But then I gave it another chance later on and the game started unfolding itself revealing more and more elements to it. It's actually interesting concept which you don't see very often.
And already there are examples of what people could do with it. To name a few, Candy Box, Candy Box 2 and Dark room added the "coffeebreak roguelike" aspects as they added the story and exploring with loot and so on. Then there is Cookie Clicker which got me hooked even though it's just about generating more and more cookies per second to buy more and more expensive upgrades that will help you generate even more cookies per second.
The guys behind cookie clicker even teamed up with adventure quest and made a game where you generate gems which you use to raise a dragons.
To answer your second question, yes it is possible to create such a game with C2. Since it's all about math, all you need is a loop and couple of variables that'd interact with each other. (Base cookies per second, some multipliers, things that'd add or deduct from the cookie bank, and events which would check whether certain cookie count was reached in order to "enable" more features for the unfolding effect).
I think there are few things to watch out for in terms of memory and CPU usage since without careful optimisation it could get out of the hand pretty fast.