For $400, you can buy a decent home sub or DIY one that will outperform the car sub.
First of all, car amps are not regulated as to how they rate them the way home electronics are. I'd seriously doubt that the amp would do much more than 200 watts according to home regulations if that - but I could be wrong.
Also remember that most 'big' car subs like that are built for pure output and not for smooth response. Most of them also don't go down much below 30Hz. Lastly, to use this setup, you'll also have to purchas a 110V to 12V converter to run the car amp.