Dude, some will scream and cry about the power and heat but If you can make it work, Go for it! It's all about ingenuity. I think your alternator ought to be fine. I don't think you'll have starting or charging trouble unless you are out posing banging music for hours with the car off running on battery.
Heck, I'm going against the grain in my new install and using one of the old socket 478 P4 2.8GHZ Prescotts I have laying in my parts stockpile simply because I'm not trying to spend a ton of $$$$ on parts, when I have so many pc parts laying around my apartment that I'm tripping over stuff when I am going to the bathroom in the middle of the night. I'm more affraid of my soundsystem leaving me stuck than the car pc .