It isn't Cool Edit that will limit you here (Cool will record loads and loads of tracks at the same time - you want 24 mics on your drum kit? Okay, Cool can handle it). The problem is your soundcard and your computer's capacity to process the massive wav files you deal with in computer recording. Soundcards come with different numbers of channels - some have 2, some have four, some have eight or ten channels. The more channels, the more expensive the card.
So the answer is yes, you can hook a mixer up to your computer via your soundcard. As for 12 channels, I've never heard of a soundcard that has that many channels, but you can buy two soundcards and run 'em together. But 12 channels? Damn, that's a lot of data for a computer to handle at one time. These audio files are really huge. I've never tracked more than four channels at a time, so I don't know what my computer would do with 12 channels, but I think it would crap out.