You don't own the original game. You pay for a license for unlimited use of the game. But one term of use is you're not allowed to use a crack to hack into it. So, yes, it is illegal to do so. I realize European courts tend to rule differently, but that's still officially what it says.
And while you have to run steam, it runs silently in the background with minimal use of the processor and can be run offline (you don't have to be online to run civ, just to activate it).