those mini-amps/amp-cards are fine for home computer usage, but will be useless in a car. they're simply not powerful enough. 10-15w will not even match a modern factory radio (if a factory radio can outperform something then you know it's bad!)
unless you're an electronics genius, I doubt you would be able to simply remove the amp from a head unit since it's integrated into the main circuitboard. but you could remove all the "guts" from the HU, remove the CD player mechanisms and mount the main circuitboard (and any other components necessary for the HU to operate) inside your PC case. IMO, this would not be worth the effort but I'm just giving you some ideas.
if you want to use a HU to amp your speakers then just keep the HU in tact and mount it in the glove box, under the dash, under a seat, etc. you don't have to take a HU apart to keep using it, just hide it somewhere