I'm not sure it would FIT...unless you don't mind giving up one passenger space. As for work, well you should just need an amp that can drive the 8ohm load.
Any car stereo amp can drive a 8ohm load. You will just have to wire it right to get the most out of your amp. Most of the class D amps(and anyother class) can go down to 2ohm and 1ohm(mostly class D) for their maximum power. You won't get much from a car amp if its at 8ohm unless you have a really powerfull amp.
Besides, I'm sure their are much better subs that are made speciffically for cars. Look into JL Audio if you like all around good sound. If you want just boomy bass look at Rockford Fosgate or Kicker. I'd much rather have JL Audio's, they seem to hit all the frequency's great. Plus I have 2 15" w4's myslef. I've also had 4-6 pairs of Rockfords and just thought they sounded terrible compared to the JL's. But I'd love to get my hands on the JL 12" w7. There's a awesome sub. But at $700 a sub it doesn't fit everyone's budget.
Car subs perform very well without large boxes due to cabin gain. I have one twelve in a slot loaded 1.25 cubic foot box and it is more than enough in my car. My Kicker has great Sound quaility and gets real loud. remember the install is 90% of the sound. Any sub will sound boomy if the box is out of spec.