In theory, any 2D game can be made with C2 so it's not limited to platformers or physic puzzle games. I also believe anything can be done in C2 but as anything it requires its fair share of effort.
In what you describe, the trickier part would be the IA.
I can think of ways to emulate it/use predefined strategy that the CPU player would apply to the situation but I don't know for sure how deep/complex you can go and how different to "regular programming" it is (I miss the experience on that in coding languages).
Tom may have more informations there as IA is a domain he should be comfortable with.
So I wouldn't definetely recommend it, but I believe there is no counter-indication to it.
Maybe the best for a start is to build a little prototype with the basics you want to have in your IA and see how well/hellish it goes so far.
If you happen to be able to produce it quickly/easily enough, then C2 should suit your project in the long run.
There are a few card games that lies in your creations forum and I believe to have seen some topics asking for help in the "how do I" forum too but I couldn't swear it's totaly relevant to your project.
But I'm afraid it's either too early (C2 is still less than a year old) or no one else took this road/posted about it yet.
I hope this answer helps you with your choice.