I understand you wanting to do something unique, but then again CTR parts in a Civic is totally different than an Integra interior. You're right, a CTR interior won't magically turn your car into an actual CTR, but at least it makes sense. Why do people swap motors and suspension parts from other Hondas, if not to make their cars more powerful and better performing like the ones that are available from the Honda factory in Japan?
I just don't see the point of an Integra interior into a Civic. It's like the multitude of pointless front and rear end conversions that you see spoken about on forums all the time. You're just taking parts from one car, and slapping them onto another, with little regard to whether it actually makes sense or looks good.
Like I said before, just because you CAN do something, doesn't mean you SHOULD do something. It's great that you have an Integra parts car to work with, and I certainly would recommend utilizing the engine and transmission, but the interior? Why?
Have you even looked at the Integra interior? It's not all that great. I have one, I know. The cupholder sucks ass, it's useless for anything but tiny little fast food cups or soda cans, and even then, they'll get in the way of the radio.
It's your car, so do what you want, but honestly, I think it's a big waste.
And just so my post isn't completely useless this time, no, I don't think the Integra dash is a direct bolt-in. It is for a 92-95 Civic, since it's the same chassis as the Integra, but to fit it in your car will probably require some modifications.