While Steam runs on Linux, I am not aware that it tries to make Windows stuff run on Linux. The Win/Lin games I've seen are ones that had native Linux versions already.
I don't know if it will even try to install Civ3. And if it does I seriously doubt it will magically work with Wine as-is. And if you have it on your machine via Steam I'm not sure how that works with Wine.
So if you can download it, you'll probably have to figure out how to start it manually with Wine. Do idea how plausible that is. I had SMAC running in Wine ages ago, but I don't think I ever tried Civ3.